With the extensive integration of nonlinear loads into power systems, severe waveform distortion of grid signals has made accurate energy metering under distorted conditions a critical challenge in power measurement technology. To address the metering inaccuracies caused by large-scale integration of nonlinear impact loads, an active power energy metering method was proposed based on adaptive wavelet basis for pulse-distorted signals. Firstly, the characteristic analysis and mathematical modeling of pulse-distorted signals were conducted. Subsequently, a wavelet basis construction method was developed under pulse distortion by maximizing signal decomposition energy in the next-level subspace, combined with particle swarm optimization (PSO) algorithm to establish the adaptive wavelet basis. The proposed basis was then employed to decompose and reconstruct pulse-distorted signals, enabling frequency-band-specific active power measurement. Finally, an experimental metering platform was established to validate the algorithm through simulations and comparative tests under three typical distortion scenarios during electric vehicle charging. Results demonstrate that the proposed method significantly outperforms conventional wavelet bases, fast Fourier transform (FFT), short-time Fourier transform(STFT), and Generalized S-transform in both effectiveness and accuracy. The achieved measurement precision meets class 1 error requirements for electricity meters, providing a novel solution for next-generation meter design.