Conventional speech enhancement (SE) algorithms are mainly designed with the aim of improving signal-to-noise levels of noisy speech signals. However, many applications consider the enhancement of speech intelligibility as the goal for an SE system. In this study, we propose a maximum speech intelligibility (MSI) post-filter that aims to enhance the intelligibility of processed speech signals. The MSI post-filter is designed to specify a weight for each frequency band of the speech signal based on the critical band importance function. To evaluate the MSI post-filter, we combine it with a recently proposed generalized maximum a posteriori spectral amplitude estimation (GMAPA) SE algorithm. In previous studies, it has been verified that GMAPA outperforms several well-known spectral restoration approaches in terms of objective evaluations and speech recognition tests. Experimental results from the present study confirm that GMAPA also provides better results in a set of subjective intelligibility tests conducted with human subjects. Moreover, the integration of GMAPA and MSI can further improve the intelligibility scores over GMAPA alone under - 10 dB to 5 dB signal-to-noise ratio conditions.