For Chen-Qi-like four-dimensional chaotic system, controllers designed with Lyapunov stability theory make synchronization errors converge to zero asymptotically. Finite-time control technique improve it, but the errors are various with initial conditions. Therefore, fixed-time control technique is applied to design an adaptive controller and parameter estimation law, try to make the drive system synchronizing with a same type response system of unknown parameters in a fixed time. which is proven theoretically. State time history diagrams and synchronization error curves are investigated by numerical simulation with various parameters and initial state values. The results show that: during chaotic motion, the effects of synchronization errors converge to zero within a fixed time is only related to system parameters, not dependent of the initial state value, and the convergence time conforms to the theoretical calculation; during periodic motion, the effects of first three synchronization errors converge to zero within a fixed time is good, their convergence time conforms to the theoretical calculation. However, the convergence time of the last synchronization error does not conform to the theoretical calculation, due to the imbalance and mismatch of the cubic nonlinear term in the system.