An adaptive sliding mode control (SMC) algorithm is developed for a missile with highly non-linear aerodynamics. Conventional SMC algorithms have inherent robustness to system model errors, but they often induce chattering of the actuator commands. An adaptive switching gain based on the Lyapunov stability theory is proposed to mitigate the chattering in the steady state. The gain varies with respect to the distance from the sliding surface. The controller with the adaptive switching gain also has robustness to system model errors and unexpected changes in aerodynamic coefficients. A control command generation method using the estimated actuator characteristics is proposed. The proposed method avoids the control performance degradation caused by actuator fault or model disagreement. The effectiveness of the proposed control algorithm is verified through numerical simulations.