The blind attack strategy based on Principal Component Analysis (PCA) is only effective for the measurement data with Gaussian noise. In the presence of outliers, the attack strategy will be detected by the traditional bad data detection module. Aiming at the problem of outliers, a blind attack strategy based on Robust PCA (RPCA) was proposed. Firstly, the attacker collected the measurement data with outliers. Then, the outliers and the real measurement data were separated from the measurement data containing outliers by the sparse optimization technique based on the Alternating Direction Method (ADM). Secondly, the PCA technique was carried out on the real measurement data, and the relevant information of the system was obtained. Finally, the acquired system information was used to construct the attack vector, and the false data was injected according to the attack vector. The experimental results show that the traditional attack method based on PCA will be detected by the bad data detection module in the presence of outliers, and the proposed method based on robust PCA can avoid the detection of bad data detection module. This strategy makes it possible to successfully implement False Data Injection Attack (FDIA) in the presence of outliers.