When labeled examples are limited and difficult to obtain, transfer learning employs knowledge from a source domain to improve learning accuracy in the target domain. However, the assumption made by existing approaches, that the marginal and conditional probabilities are directly related between source and target domains, has limited applicability in either the original space or its linear transformations. To solve this problem, we propose an adaptive kernel approach that maps the marginal distribution of target-domain and source-domain data into a common kernel space, and utilize a sample selection strategy to draw conditional probabilities between the two domains closer. We formally show that under the kernel-mapping space, the difference in distributions between the two domains is bounded; and the prediction error of the proposed approach can also be bounded. Experimental results demonstrate that the proposed method outperforms both traditional inductive classifiers and the state-of-the-art boosting-based transfer algorithms on most domains, including text categorization and web page ratings. In particular, it can achieve around 10% higher accuracy than other approaches for the text categorization problem. The source code and datasets are available from the authors.