This paper describes a new design of the Wiener post-filter for diffuse noise suppression. The Wiener post-filter is well-known as an effective post-processing of the minimum variance distortionless response beamformer, and its output is the optimal estimate of the target signal in the sense of the minimum mean square error. It is essential to accurately estimate the target power spectrum from the observed signals contaminated by noise when designing the Wiener post-filter. In our method, it is estimated from the imaginary parts of the inter-channel observation cross-spectra, under the assumption that the inter-channel noise cross-spectra are real-valued. The post-filter is designed using the estimate and this design is shown to be effective even for a small-sized array through experiments using simulated and real environmental noise.