Magnetic heterostructure Mo/CoFeB/MgO has strong perpendicular magnetic anisotropy and thermal stability. Through current-induced hysteresis loop shift measurements, we show that the dampinglike spin-orbit torque (SOT) efficiency of Mo/CoFeB/MgO heterostructure is $\xi_{DL}\approx -0.003\pm 0.001$ and fairly independent of the annealing temperature from 300$^\circ$C to 400$^\circ$C. Though $|\xi_{DL}|$ is small while compare to those from Ta or W-based heterostructures, reversible current-induced SOT switching of a thermally-stable Mo/CoFeB/MgO heterostruture can still be achieved. Furthermore, we observe field-free current-induced switching from a Mo/CoFeB/MgO structure with the Mo layer being wedge-deposited. Our results indicate that even for a weak spin-orbit interaction 4d transition metal such as Mo, it is still possible to generate sufficient spin current for conventional SOT switching and to realize field-free current-induced switching by structural engineering.