This paper presents our approach for automatic speech recognition (ASR) of overlapping speech. Our system consists of two principal components: a speech separation component and a feature estmation component. In the speech separation phase, we first estimated the speaker's position, and then the speaker location information is used in a GSC-configured beamformer with a minimum mutual information (MMI) criterion, followed by a Zelinski and binary-masking post-filter, to separate the speech of different speakers. In the feature estimation phase, the neural networks are trained to learn the mapping from the features extracted from the pre-separated speech to those extracted from the close-talking microphone speech signal. The outputs of the neural networks are then used to generate acoustic features, which are subsequently used in acoustic model adaptation and system evaluation. The proposed approach is evaluated through ASR experiments on the {\it PASCAL Speech Separation Challenge II} (SSC2) corpus. We demonstrate that our system provides large improvements in recognition accuracy compared with a single distant microphone case and the performance of ASR system can be significantly improved both through the use of MMI beamforming and feature mapping approaches.