A hyperspectral image sequence can be obtained at different time in the same region from a hyperspectral sensor. The environmental change usually leads to variation in endmember reflectance, which has an important influence on unmixing process. In this article, a Bayesian unmixing model considering spectral variability for hyperspectral sequence is proposed, in which composite prior distributions of abundance and endmember variability are developed. The abundance priors consider the continuity of abundance in the temporal and spatial domains, simultaneously. Specifically, in the spatial domain, a data-adaptive variance of the abundance prior distribution is put forward based on local spatial difference. Moreover, the priors of endmember variability in temporal continuity and spectral smoothness are also exploited. Finally, a joint posterior distribution is obtained by the likelihood function and the parameter prior distributions, which can be calculated by the Markov chain Monte Carlo (MCMC) algorithm. Experiments on synthetic and real data sets demonstrate the effectiveness of the proposed approach in terms of abundance, endmember, and its variability estimation accuracy.