Tensor model-based parameters estimation is a trend for radar signal processing. However, the existing tensor-model based algorithms cannot achieve a good compromise between estimation accuracy and computational complexity. A three-way compressive sensing (TWCS) based algorithm is developed for angle estimation in multiple-input multiple-output radar. Exploiting the multidimensional structure inherent in the matched filtered data, a third-order tensor signal model is formulated. To lower the storage and computing complexity, the high-order singular value decomposition method is used to compressive the tensor data. The kernel tensor is linked to the trilinear model thus the compressed direction matrixes are obtained. Thereafter, the sparsity of the targets in the background is utilized and two overcomplete dictionaries are constructed for angle estimation with optimization methods. Taking advantage of the inherent multidimensional structure of the received data, the TWCS algorithm achieves better estimation accuracy than traditional subspace-based algorithms. In addition, the TWCS algorithm does not require further pairing of the estimated angles. Furthermore, it could achieve the doppler frequencies of the targets. Simulation results verify the effectiveness of the TWCS algorithm.