Abstract: Natural supercavity shape and its drag reduction at small cavitation number have been numerically simulated with Finite Difference code CFD. User-Defined Functions (UDFs) for the time-dependent free stream velocity was implemented into CFD software. The effects of acceleration on natural supercavity shape and its drag reduction have been obtained. With the same cavitation number, the thickness and length of supercavity are smaller at positive acceleration than those at zero acceleration, and larger than those at negative acceleration. Viscous drag coefficient has no direct relations with acceleration, which is mainly related to supercavity shape and vapor volume fraction in supercavity. The numerical results are compared with the experimental results at acceleration of -100 m/s2, and the maximal error does not exceed 35%.