Projective synchronization control of the Arneodo system and Coullet system is present in this paper. The Arneodo system is the drive system and the Coullet system is the response system. The state variables corresponding to the Arneodo system and Coullet system are synchronized to scaling factor. A single adaptive controller based on sliding mode control theory is used to control the projective synchronization error signals, and the error signals converge to zero rapidly, thereby achieving projection synchronization control of the Arneodo system and the Coullet system. The stability of the designed adaptive controller has been theoretically proven, and numerical simulation has been conducted using MATLAB software. The hyperbolic tangent function is applied in the adaptive controller to reduce the chattering. The simulation results show that the adaptive controller can perform projection synchronization control of the Arneodo system and the Coullet system, and the results are analyzed in the end.