In this paper, a novel small target detection algorithm based on robust master analysis (RPCA) is proposed to solve the problem of small target difficult to detection in single infrared image. Because of the background matrix is a low rank matrix and the target matrix is a sparse matrix, small target detection can be formulated as an optimization problem of recovering low-rank and sparse matrices. RPCA method is used to restore the background matrix and targets matrix, and then choose the inexact augmented Lagrange multipliers to solve RPCA model which is faster. At last, two simulation experiments result indicate that can adapt to a variety of single image and the timeliness is good for small matrix.