This paper proposes a novel approach to robust principal component analysis (PCA). It first searches for a subset of most reliable inliers from original data by projection pursuit. We define an index function for each projection direction and utilize a nonparametric mode search technique, the mean shift, to obtain the index value. The inlier subset is identified from data projections on the direction with highest index. We discover the initial principal subspace from the inlier subset, and project all the data onto that subspace. The outliers are then detected based on the analysis of the squared prediction error (SPE) of each sample, which measures the distance between the sample and its projection on that subspace. Experimental results on both synthetic data and a real image set illustrate the effectiveness of our approach in removing outliers and obtaining the reliable PCA solution.