Universal Background Model (UBM) has been successfully applied to many speech signal classification tasks, such as speaker recognition and microphone recognition. UBM is used to form Gaussian Supervector (GSV) or i-vector, which is a good feature vector representing a piece of speech signal. In this paper, we propose another background model called Class-dependent Background Model (CBM), which makes use of class labels. UBM is completely a generative model, while CBM can be both generative and discriminative. Under some conditions, CBM can consume less time to be constructed than UBM. We also compare the performance of UBM and CBM as the background model to form GSV and i-vector for doing speaker recognition, microphone recognition, and telephone session recognition. Experimental results show that CBM performs very well and can be even better than UBM in most cases.