The adaptive Fourier decomposition (AFD) is a greedy iterative signal decomposition algorithm in the viewpoint of energy. Instead of using a fixed basis for decomposition, AFD uses an adaptive basis to achieve efficient energy extraction. In the conventional searching method, a new basis is searched from a large dictionary at every decomposition level. This usually results in a slow searching speed. To improve the efficiency, a fast searching method based on Nelder-Mead algorithm is proposed in this paper. The AFD with the proposed searching method is applied for electrocardiography (ECG) signals in which the selection ranges of four key parameters in the proposed searching method are determined based on simulation results of an artificial ECG signal. The simulation results of real ECG data shows that the computational time of the AFD based on the proposed searching method is just half of that based on the conventional searching method with similar reconstruction error.