Appling pre-defined-time stability theory, three controllers were designed to achieve synchronization between Chen-Qi-like four-dimension hyper-chaotic driving systems and response systems of the same type with unknown parameters within a pre-defined time based on tangent function, hyperbolic tangent function, or exponential function. Theoretical proofs were provided. Its’effectiveness were testified with state time history diagrams and synchronous error curves via numerical simulation. The results indicated that controllers designed can achieve to synchronize to chaotic motion while the driving system in chaotic motion, and with a small convergence time difference among the four state synchronization errors. But there was a significant convergence time difference in the four state synchronization errors while driving system in periodic motion. That was induced by the imbalance and mismatch of the state cubic nonlinear term essentially. The results also indicated that adaptive controller and parameter correction law based on tangent function had a larger range of adaptability to initial state values and system parameters comparing to the other two controllers and parameter adaptive laws, thus it hold a better universality.