In view of the performance degradation in impulsive noise environment due to the non- existence of the second-order moment, an estimation algorithm based on orthogonal trigonometric(QR)- Robust Principal Component Analysis(QR-RPCA) in bi-static ultiple-Input-Multiple-Output(MIMO) radar is proposed. At first, the complex received signal is converted into real-value for the RPCA algorithm. After that, according to the sparsity of impulsive noise and the low rank of signal matrix, the QR-RPCA algorithm is utilized to extract the low-rank signal matrix from the received signal polluted by impulsive noise and acquire the signal subspace directly. The QR-RPCA algorithm averts solving large-scale Singular Value Decomposition(SVD) and reduces the complexity relative to other traditional algorithms. Finally, Estimating Signal Parameters via Rotational Invariance Techniques(ESPRIT) are adopted to obtain the target locations. The theory and the simulation show that the proposed method has better estimation performance than the traditional ones in impulsive noise elimination while the characteristic index of impulsive noise is low.