Phase-shifting shearography interferometry needs to extract dynamic phase of the measured object after loading, so the random phase-shifting speckle patterns analysis algorithm based on principle component analysis (PCA) is proposed. By using the correlation method, the fringe patterns with random phase shifts are obtained from the speckle patterns with random phase shifts. Then the dynamic phase distributions are extracted from one set of random phase-shifting fringe patterns by PCA. Experimental results show that the obtained fringe patterns have high signal-to-noise ratio, and the extracted phases are accurate and efficient. The proposed method is non-iterative and has no strict requirement for the spatial-carrier frequency of fringe patterns, so it is suitable for dynamic shearing speckle interferometry.