This paper presents a general Bayesian model for speaker verification tasks. It is a generative probability model. Due to its simple analytical property, a computationally efficient expectation-maximization algorithm can be derived to obtain the model parameters. A closedform solution, which allows the scalable size of enrollment set, is given in a full Bayesian way for making speaker verification decisions. Factor analysis technique is employed to model the speaker-specific components, then the redundant information in this model will be dropped. Experimental results are evaluated by both equal error rate and minimum detection cost function. The proposed approach shows promising results on the National institute of standards and technology(NIST) Speaker recognition evaluation(SRE) 2010 extended and 2012 core tasks. Significant improvement is obtained when comparing with Gaussian probabilistic linear discriminant analysis, especially under phone-call conditions and mismatched train-test channel conditions. Contrast experimental results with other popular generative probability models are also presented in this paper. Due to its simple analytical property, a computationally efficient expectation-maximization algorithm can be derived to obtain the model parameters. A closedform solution, which allows the scalable size of enrollment set, is given in a full Bayesian way for making speaker verification decisions. Factor analysis technique is employed to model the speaker-specific components, then the redundant information in this model will be dropped. rate and minimum detection cost function. The proposed approach shows promising results on the National institute of standards and technology (NIST) Speaker recognition evaluation (SRE) 2010 extended and 2012 core tasks. Significant improvement is obtained when comparing with Gaussian probabilistic linear discriminant analysis, especially under phone-call conditions and mismatched train-tes t channel conditions. Contrast experimental results with other popular generative probability models are also presented in this paper.