Since the spatially colored noise covariance matrix of multiple input multiple output (MIMO) radar is an off-diagonal matrix, the signal subspace and the noise subspace cannot be separated effectively under colored noise, which results in the problem that the traditional angle estimation algorithm cannot estimate the target angle correctly. Therefore, the low-rank property of the signal covariance matrix and the sparsity of the colored noise covariance matrix were utilized to suppress the spatially colored noise. Then, according to the multi-dimensional structure characteristics of MIMO radar data, the fourth-order tensor CP (canonical or parallel factor analysis, CANDECOMP/PARAFAC) decomposition model was established. To solve the problem that the traditional alternating least squares algorithm is sensitive to numerical ill-conditioning, which leads to the low precision of CP decomposition, the conjugate relationship between tensor factor matrices was used to reduce the ill-conditioning sensitivity of the solution and improve the robustness of tensor decomposition. Finally, the least square fitting method was used to obtain the target angle from the estimation of the factor matrices. The simulation results indicated that our algorithm is capable of suppressing the colored noise adequately and improving the precision of angle estimation.