Dictionary learning has produced state-of-the-art results in various classification tasks. However, if the training data have a different distribution than the testing data, the learned sparse representation might not be optimal. Recently, several domain-adaptive dictionary learning (DADL) methods and kernels have been proposed and have achieved impressive performance. However, the performance of these single kernel-based methods heavily depends heavily on the choice of the kernel, and the question of how to combine multiple kernel learning (MKL) with the DADL framework has not been well studied. Motivated by these concerns, in this paper, we propose a multi-kernel domain-adaptive sparse representation-based classification (MK-DASRC) and then use it as a criterion to design a multi-kernel sparse representation-based domain-adaptive discriminative projection method, in which the discriminative features of the data in the two domains are simultaneously learned with the dictionary. The purpose of this method is to maximize the between-class sparse reconstruction residuals of data from both domains, and minimize the within-class sparse reconstruction residuals of data in the low-dimensional subspace. Thus, the resulting representations can satisfactorily fit MK-DASRC and simultaneously display discriminability. Extensive experimental results on a series of benchmark databases show that our method performs better than the state-of-the-art methods.