To meet the new requirements for mobile robots in the field of modern engineering and expand the working opportunities of mobile robots, a spherical parallel leg mechanism of a wheel-leg composite mobile robot was proposed in this study. First, based on the closed-loop constraint equation and rotation transformation matrix of the spherical parallel leg mechanism, a mathematical model of its inverse position solution was constructed. Next, an analytical solution of the forward position solution of the spherical parallel leg mechanism was deduced by the algebraic elimination method. Then, the influence coefficient matrix of the velocity and acceleration of the spherical parallel leg mechanism was derived from the influence coefficient method. On this basis, the Lagrangian method was used. Kinematics and dynamics models were validated by numerical simulation. The maximum error between the given and calculated position data was 0.012 7 rad, and the error did not exceed 2.43% of the actual value. It is also found that the theoretical curve of the driving force of the spherical parallel leg mechanism coincided with the simulation curve of the virtual prototype. The error between the two was stable within a reasonable range of 0-1 N. The correctness of the kinematics and dynamics model is proved. The results from this study provide a theoretical reference for gait planning and motion control of a wheel-leg hybrid mobile robot.