Narrow-band interference (NBI) is a critical issue for synthetic aperture radar (SAR), in which the imaging quality can be degraded severely. To suppress NBI effectively, a novel interference suppression algorithm using robust principal component analysis (RPCA) based signal separation in time-frequency domain is proposed. The RPCA algorithm is introduced for signal separation in the time-frequency domain for the first time. The fundamental assumption of RPCA is that a matrix can be modeled as a combination of a low-rank matrix and a sparse counterpart. In terms of the SAR echo, the short time Fourier transformation (STFT) matrix of mixed signals (i.e., useful SAR signals and NBIs) well fits the assumption of RPCA. Based on this property, radar echoes are first transformed into the time-frequency domain by STFT to form an STFT matrix. Then, the RPCA algorithm is used to decompose the STFT matrix into a low-rank matrix (i.e., NBIs) and a sparse matrix (i.e., useful signals). Finally, the NBIs can be reconstructed and subtracted from the echoes to realize the interference suppression. The experimental results of simulated and measured data demonstrate that the proposed algorithm not only can suppress interference effectively, but also preserve the useful information as much as possible.