Focusing on the issue that the data acquisition amount of Photoacoustic Computed Tomography (PACT) based on ultrasonic array is generally huge, and the imaging process is time-consuming, a fast photoacoustic computed tomography method with Principal Component Analysis (PCA) was proposed to extend its applications to the field of hemodynamics. First, the matrix of image samples was constructed with part of full-sampling data. Second, the projection matrix representing the signal features could be derived by the decomposition of the sample matrix. Finally, the high-quality three-dimensional photoacoustic images could be recovered by this projection matrix under three-fold under-sampling. The experimental results on vivo back-vascular imaging of a rat show that, compared to the traditional back-projection method, the data acquisition amount of PACT using PCA can be decreased by about 35%, and the three-dimensional reconstruction speed is improved by about 40%. As a result, both the fast data acquisition and high-accurate image reconstruction are implemented successfully.