In this paper, we investigate the anti-synchronization between a class of chaotic real nonlinear systems and a class of chaotic complex nonlinear systems with fully uncertain parameters. According to Lyapunov stability theory, an adaptive control scheme and adaptive laws of parameters have been designed to realize the anti-synchronization between a class of chaotic real nonlinear systems and a class of chaotic complex nonlinear systems with different initial conditions. The anti-synchronization between the real Lorenz system and the complex Lorenz system, the real Chen system and the complex Lü system are presented as two examples to demonstrate the validity and feasibility of the presented control technique.