In this letter, we present an adaptive weighted transfer subspace learning (AWTSL) method for cross-database speech emotion recognition (SER), which can efficiently eliminate the discrepancy between source and target databases. Specifically, on one hand, a subspace projection matrix is first learned to project the cross-database features into a common subspace. At the same time, each target sample can be represented by the source samples by using a sparse reconstruction matrix. On the other hand, we design an adaptive weighted matrix learning strategy, which can improve the reconstruction contribution of important features and eliminate the negative influence of redundant features. Finally, we conduct extensive experiments on four benchmark databases, and the experimental results demonstrate the efficacy of the proposed method.