The goal for most speech enhancement techniques is to improve speech quality by increasing intelligibility and/or reducing listener fatigue. The Multi-microphone Sub-band Adaptive (MMSBA) processing scheme has been shown to improve both the SNR and speech intelligibility of a wanted speech source in the presence of an unwanted noise source, in a moderately reverberant real-room environment using two microphones [1]. The proposed Sub-band Adaptive Griffiths-Jim (SBAGJ) processing scheme uses features from the Griffiths-Jim [2] adaptive noise canceller, in conjunction with the MMSBA scheme. The combination of the Griffiths-Jim front end, and the MMSBA noise cancelling section results in a system with the improved filter performance of a sub-band processing scheme, but bypasses the need to explicitly deal with the causality issues associated with many adaptive noise cancellation algorithms.