The equalization-cancellation (EC) model has been extensively studied for expressing binaural masking level difference (BMLD) in psychoacoustics. Few research focuses on applying this psychoacoustic model to speech processing applications, such as speech enhancement. In this paper, we propose a two-stage binaural speech enhancement with Wiener filter (TS-BASE/WF) based on the EC model. In this proposed TS-BASE/WF, interfering signals are first estimated by equalizing and cancelling the target signal based on the EC model, and a time-variantWiener filter is then applied to enhance the target signal given noisy mixture signals. The main advantages of the proposed TS-BASE/WF are: (1) effectiveness in dealing with non-stationary multiple-source interfering signals; (2) success in localizing the target sound source after processing. These advantages were confirmed by comprehensive experiments in different spatial scenarios in terms of speech enhancement and sound localization.