A guidance law with finite time convergence is designed using the sliding mode control method and finite time convergence control theory, accounting for the missile autopilot as second-order dynamics. The high-order derivatives of the line of sight (LOS) angle are avoided in the expression of guidance law such that it can be implemented in practical applications. The designed guidance law is effective in compensating the bad influence of the autopilot dynamics on guidance accuracy. In simulations of intercepting a non maneuvering target or a maneuvering target, respectively, the designed guidance law is compared with the adaptive sliding mode guidance (ASMG) law in the presence of missile autopilot lag. Simulation results show that the designed guidance law is able to guide a missile to accurately intercept a nonmaneuvering target or a maneuvering target with finite time, even if it escapes in a great and fast maneuver and the autopilot has a relatively large lag.