In this study, we propose increasing discriminative power on the maximum a posteriori (MAP)-based mapping function estimation for acoustic model adaptation. Based on the effective and stable learning advantages of MAP-based estimation, we incorporate a discriminative term and derive a new objective function. By applying the new function for online mapping function estimation, we developed discriminative maximum a posteriori (DMAP) linear regression (DMAPLR) and DMAP-based ensemble speaker and speaking environment modeling (DMAP-based ESSEM). We evaluate the DMAPLR and DMAP-based ESSEM on the Aurora-2 task in a supervised adaptation mode. The experimental results show that both DMAPLR and DMAP-based ESSEM consistently provide improvements over their ML-based and MAP-based counterparts irrespective of using one, two, or three adaptation utterances. From the improvements, we confirm the strong effect of increasing discriminative capability on the MAP-based mapping function estimation. Mo...