An output-feedback discrete sliding mode control based on unbiased state estimation is proposed for industrial control systems under actuator attack and measurement noisy. In the presence of actuator attack, an equivalent sliding mode control law is constructed. Since the attack signal and the state of the system are unknown, an unbiased state observer is introduced to provide the minimum variance unbiased estimator of the system real state from the sensor measurement data subject to noise interference. In order for the designed robust sliding mode control algorithm to be implemented, a one-step delay attack estimation is introduced to obtain the approximate estimate of attack. The convergence of the sliding surface and the bounded stability of the closed-loop system under the proposed control algorithm is proved. Numerical simulation results demonstrate the effectiveness of the unbiased state estimator, and show that compared with the traditional sliding mode control method, the proposed output feedback sliding mode control algorithm has better suppression for the actuator attack and can effectively improve the robustness of the system.