Creep crack growth (CCG) analysis is extremely important for integrity evaluation of the defective structures at elevated temperatures in a thorium molten salt reactor (TMSR). However, a numerical method of CCG analysis that can be applied to the TMSR has not yet been developed. In this study, the CCG behavior of a UNS N10003 alloy was investigated based on the Liu and Murakami (L-M) creep damage model. First, the material constants were obtained according to the uniaxial creep test data. Second, finite element analysis (FEA) of CCG for compact tensile (CT) specimens was conducted, and the influence of factors such as element meshing, crack tip radius, side groove, and fillet was analyzed. The results indicated that the crack tip radius and fillet at the side groove demonstrated a significant effect on the accuracy and rationality of the FEA model. Moreover, the multi-axial parameter α in the L-M model was obtained by comparing the calculated results with the CCG test data. The calculated results were found to be more conservative than the experimental results. Finally, the proposed numerical analysis method was applied to the CCG life-span prediction of the pressure vessel in the TMSR. Thus, this study suggests an effective, reliable numerical method for CCG behavior prediction of the UNS N10003 alloy, which has important engineering significance for structural integrity evaluation at elevated temperatures in the TMSR.