In this paper, we provide a new framework to study the generalization bound of the learning process for domain adaptation. Without loss of generality, we consider two kinds of representative domain adaptation settings: one is domain adaptation with multiple sources and the other is domain adaptation combining source and target data. In particular, we introduce two quantities that capture the inherent characteristics of domains. For either kind of domain adaptation, based on the two quantities, we then develop the specific Hoeffding-type deviation inequality and symmetrization inequality to achieve the corresponding generalization bound based on the uniform entropy number. By using the resultant generalization bound, we analyze the asymptotic convergence and the rate of convergence of the learning process for such kind of domain adaptation. Meanwhile, we discuss the factors that affect the asymptotic behavior of the learning process. The numerical experiments support our results.