This paper investigates the fixed time control and synchronization of chaotic system in the presence of compound disturbances. By using the definite integration and variable substitution, we present a new fixed time stability theorem for continuous nonlinear systems. In order to offset the bad effects of the compound disturbance, some novel sliding modes are constructed to improve the robustness of the controlled system and error system. For obtaining the robust controllers, some sufficient conditions of fixed time control and synchronization of the chaotic system are proposed by means of the sliding mode control method and the given stability theorem. Numerical simulation results are presented to verify and demonstrate the effectiveness of the proposed schemes.