This article is related to the issue of fixed-time synchronization of different dimensional complex network systems with unknown parameters. Two suitable adaptive controllers and dynamic parameter estimations are proposed such that the complex network driving and response systems can be synchronized in the settling time. Based on fixed-time control theory and Lyapunov functional method, novel sufficient conditions are provided to guarantee the synchronization within the fixed times, and the settling times are explicitly evaluated, which are independent of the initial synchronization (...) errors. Finally, a numerical example is given to illustrate the effectiveness of the proposed control algorithms. (shrink)