The recursive correlation method is widely used in the particle image velocimetry technique. However, it has a problem that the number of outliers increases as the size of the correlation window decreases for obtaining the high-resolution velocity field. Therefore, we propose gappy robust principal component analysis (RPCA) which estimates the most probable velocity field by extending standard RPCA which reduces the dimension of data removing outliers. The proposed method improves the high-resolution estimation of the turbulent flow velocity field. The proposed method was verified with synthetic particle images of the separated flow around an airfoil. As a result, the error of the proposed method is lower than the conventional recursive cross-correlation method by 37.82%.