Abstract: ‍ ‍To solve the problem that the training and testing data come from different domain databases in actual situation， which leads to the decline of recognition performance， we proposed a transfer discriminant regression method for cross-domain speech emotion recognition. Specifically， first， we employed maximum mean discrepancy （MMD） and graph Laplacian as the distance measurement between domains to reduce the distribution difference while preserving the local geometrical structure. Thus， we can learn a transferable common feature representation. To ensure that the information of target corpus is not lost in the process of knowledge transfer， an energy conservation strategy was proposed. Second， we trained a transferable regression model by using labeled source domain samples in the common subspace. We imposed an ${\mathrm{L}}_{\mathrm{2,1}}$-norm constraint on the common projection matrix and regression term， which can make the model be more robust. The experimental results on three public datasets show that the proposed approach outperforms the other transfer learning methods.