We combine the parallel factor framework with the compressed sensing theory to solve the problem of the direction of arrival estimation for the electromagnetic vector sensor array. We first rearrange the received data matrix as a parallel factor model, and compress it to a smaller one based on the compressed sensing theory. Then the trilinear alternating least square algorithm is exploited to decompose the compressed parallel factor model. Finally, the angle estimation is obtained with sparsity. Owing to compression, the computational complexity of the algorithm is lower than that of the conventional parallel factor model-based algorithm, and more storage memory is saved. The algorithm needs no peak searching and is applicable to both uniform and non-uniform linear array. Moreover, the angle estimation performance of the proposed algorithm is better than that of the ESPRIT algorithm and close to that of the conventional parallel factor model-based algorithm, which can be verified by various simulations.