Along with the popularization of cellular phone, it becomes important issue to improve recognition accuracy for cellular phone speech input. However, the distortion caused by current low-bit rate speech corder is nonlinear. Therefore, it is difficult to compensate these distortion by only applying conventional CMN which assuming distortion as stationary linear transfer on spectrum domain. In this paper, to improve the accuracy of speech recognition over cellular-phone network, we investigate the use of CODEC-dependent acoustic model and rapid CODEC-adaptation using model selection based on maximum likelihood criterion. These method reduce degradation of recognition performance due to difference in CODEC by 33%.