Hat-shaped steel members are widely used in solar greenhouses, due to their low cost, fast construction, and high material efficiency. This study aims to determine the ultimate bearing capacity of a solar greenhouse with the hat-shaped steel under snow loads. The typical solar greenhouse with an 8m span and 3.8 m ridge height was selected as the research object. The finite element method (FEM) under ANSYS software was used to analyze the instability mechanism and failure modal of the structure under snow loads (uniform and non-uniform snow loads). An investigation was made to clarify the effects of the longitudinal tie bars, initial geometric imperfections, and sectional dimensions on the ultimate bearing capacity of the structure under non-uniform snow loads. Both the material and geometrical nonlinearity were considered in the finite element model. A bilinear kinematic hardening model was adopted for the steel with a yield strength of 235 MPa, Young's modulus of 206 GPa, and Poisson's ratio of 0.3. The geometrical nonlinearity was activated using the 'NLGEOM' option. To consider the local buckling, the greenhouse skeletons were then modeled with the Shell181 element suitable for the large strains and rotations. Fixed hinge supports were used for both ends of the skeleton. An arc-length method was utilized to trace the nonlinear load-displacement curve, in order to calculate the ultimate bearing capacity of the structure under snow loads. The ultimate bearing capacity of the solar greenhouse with the hat-shaped steel was slightly higher than that of the hollow rectangular section under the same conditions of net section area, upper flange width, web depth, and wall thickness. The solar greenhouse was more sensitive to the non-uniform snow loads, compared with the uniform ones. The ultimate bearing capacity of the hat-shaped steel solar greenhouse under non-uniform snow loads was about 28% of that under uniform snow loads. Therefore, some suggestions were presented for the non-uniform snow loads in the design stage of the solar greenhouse structure. The roof ridge and north roof end were dangerous sections under non-uniform snow loads, which firstly entered the full section yield state. The longitudinal tie bars were expected to effectively improve the ultimate bearing capacity of the greenhouse structure. The ultimate bearing capacity of the structure with the longitudinal tie bars was about 1.25 times that without tie bars. The ultimate bearing capacity was only reduced by 2%, when the initial geometric imperfections amplitude increased from 5 to 20 mm. It infers that the solar greenhouse was not sensitive to the initial geometric imperfection. The cross-section size of a hat-shaped steel was recommended that the ratio of the upper flange width to the lip width, the upper flange width to the lower flange width, and the web depth to the lower flange width were about 4.17, 3.33, and 4.67, respectively, while, the ratio of the web depth to the lip width, and the lower flange width to lip width were less than 9.25 and 1.7, respectively. These findings can provide a strong reference for the solar greenhouse with the open cold-formed thin-walled steel under snow loads.