Nuclear graphite is the primary structural material of reactor core in the high temperature gas-cooled reactor. It is of great significance for the research of the graphite's fracture property and the analysis of the crack propagation process to analyze the structural integrity of graphite component. The filtering method based on radial basis function (RBF) is suitable for electronic speckle pattern interferometry (ESPI) speckle patterns with low density. A kind of phase measuring method base on RBF filtering and quality-guided phase-unwrapping algorithm is proposed, then this method is tested via application to computer-simulated ESPI phase pattern and compared with the average filtering quantitatively. ESPI technique and three-point bending tests are employed to measure the fracture property of nuclear graphite specimen with pre-cracking. The ESPI wrapping phase patterns are recorded with different loads in the evolutionary process of crack, and the phase contours are extracted by the use of RBF filtering method and quality-guided phase-unwrapping algorithm, then the evolutionary process sketch map of the specimen is given. The experimental results demonstrate that this method is effective to measure the crack evolutionary process of nuclear graphite.