All observation has uncertainty due to noise or channel characteristics. This uncertainty should be counted in the modeling of observation. In this paper we propose a modified optimization object function of a GMM training considering inexact observation. The object function is modified by introducing the concept of observation confidence as a weighting factor of probabilities. The optimization of the proposed criterion is solved using a common EM algorithm. To verify the proposed method we apply it to the speaker recognition domain. The experimental results of text-independent speaker identification with VidTimit DB show that the error rate is reduced from 14.8% to 11.7% by the modified GMM training.