The disturbance decoupling-based fixed-time and predefined-time fault estimation issues are addressed for complex networks. A distributed fixed-time fault estimation observer subject to two power functions is first constructed, which can not only eliminate the effect of external disturbances but also identify unknown faults in a fixed time. Then, a nonlinear fixed-time fault estimator with two power functions, including state residuals, is presented to enhance the convergence speed of fault estimation. Furthermore, the predefined-time design strategy is investigated to assure the convergence of fault estimation errors in the specified time in advance. Finally, simulation results of complex networks of chaotic systems are shown to verify the advantage of the presented fixed-time and predefined-time schemes.