Velocity distribution of cross-section in open channel is not only the basis of accurate measurement of flow rate, but also the basic problem of studying the hydraulic characteristics of open channel. In order to explore the cross-sectional velocity distribution of partially-filled flow in circular pipe, a 3-D turbulent mathematical model and numerical solution method, verified by measured data, were adopted to simulate the partially-filled flow in circular pipe with different combinations of slopes and filling ratios. By comparison of the measured values and calculated values, the results showed that in a circular pipe with diameter 0.4 m, bottom slope 0.004, and flow rate 0.246 m3/s (corresponding filling ratio 0.47), the maximum relative error between the calculated velocities and measured values on all vertical lines was within the plus or minus 4.2%, and the maximum relative error between the calculated turbulent kinetic energy and measured values on all vertical lines was within the plus or minus 4.85%, suggesting that mathematical model and its parameters for simulation of the velocity distribution had higher calculation accuracy. The simulation results showed that cross-sectional velocity distribution was very sensitive to the filling ratio. The larger filling ratio would lead to more obvious dip phenomenon of maximum vertical velocity. When the filling ratio was lower than 0.5, no dip phenomenon occurred. When the filling ratio exceeded 0.5, the dip phenomenon became more obvious. This was because when the filling degree exceeded 0.5, the constraint effect of the side wall on the water surface was enhanced, and the secondary flow in the section was more obvious. There also showed obvious differences in the forms of vertical velocity distribution at different transverse positions, especially those close to the boundary wall, which was caused by the enhanced constraint effect of the concave side wall. Vertical profiles of time-averaged longitudinal velocity among various cases had very good similarity, and the profile curves were close to the feature of parabolic function. Influenced by factors such as section geometry and hydraulic characteristics, although the velocity distribution of each vertical line had a good similarity, the empirical coefficients by parabolic regression analysis that determined the shape of the velocity distribution curve on the specific vertical line had changed a lot. Multi-factor analysis of variance was conducted to the undetermined coefficients in parabolic function, which showed they were mainly affected by transverse position of vertical lines and filling ratio of cross section. According to the affecting degree of filling ratio and transverse position to the empirical coefficients, the cross sections of the partially-filled flow were divided into the central areas and the side wall areas along the transverse direction. Moreover, the dividing lines between central area and side wall area when the filling ratio was less than 0.5 was different from that when the filling ratio was greater than 0.5. Analysis of variance showed that the empirical coefficients of the central area were linearly correlated with the transverse position and the filling ratio, while the coefficients of the side wall area were mainly affected by the transverse position of the vertical line, and basically independent of the filling ratio. By means of regression analysis, the velocity parabolic distribution formula on vertical lines in partially-filled flow were established, and the determination methods of each coefficients were given. The calculated values of vertical velocity distribution areas were in good agreement with the measured values, which indicated that the parabolic vertical velocity distribution law was reliable. Parabolic function could better reflect the velocity distribution along vertical lines of partially filled flow in circular pipe. Application of the parabolic function to obtain flow rate on cross section, cannot only overcome the irrationality of Manning formula, but also was more easier than logarithmic law to be used in engineering calculation.