Cross-corpus speech emotion recognition has recently received considerable attention due to the widespread existence of various emotional speech. It takes one corpus as the training data aiming to recognize emotions of another corpus, and generally involves two basic problems, i.e., feature matching and feature selection. Many previous works study these two problems independently, or just focus on solving the first problem. In this paper, we propose a novel algorithm, called feature selection based transfer subspace learning (FSTSL), to address these two problems. To deal with the first problem, a latent common subspace is learnt by reducing the difference of different corpora and preserving the important properties. Meanwhile, we adopt the l_2,1-norm on the projection matrix to deal with the second problem. Besides, to guarantee the subspace to be robust and discriminative, the geometric information of data is exploited simultaneously in the proposed FSTSL framework. Empirical experiments on cross-corpus speech emotion recognition tasks demonstrate that our proposed method can achieve encouraging results in comparison with state-of-the-art algorithms.