We investigated the effect of substrate misfit strain on the current-induced magnetization switching in magnetic tunnel junctions by combining micromagnetic simulation with phase-field microelasticity theory. Our results indicate that the positive substrate misfit strain can decrease the critical current density of magnetization switching by pushing the magnetization from out-of-plane to in-plane directions, while the negative strain pushes the magnetization back to the out-of-plane directions. The magnetic domain evolution is obtained to demonstrate the strain-assisted current-induced magnetization switching.