Abstract:A projective synchronization of chaotic complex system was investigated. First, the cross projective synchronization (the real part and the imaginary part synchronize up to different scaling factors, respectively) in coupled partially linear complex nonlinear dynamic system was realized without adding any control term. Then, we investigated the substantial conditions of projective synchronization of chaotic complex systems on whole state variable with time delay. The adaptive controllers were designed. Moreover, numerical simulations were given to confirm the analytical results.