Leakoff has been regarded as the main factor that limits fracture propagation and live acid penetration distance in acid fracturing. Reducing acid leakoff is a common measure to increase effective fracture length. Due to cleanness and leakoff reduction, clean self-diversion acid (VES: viscoelastic surfactant acid) has been used in acid fracturing. So far the mechanism of leakoff reduction by VES acid is interpreted qualitatively, and performance evaluation of leakoff reduction is based on laboratory results. However, laboratory results cannot be generalized to formation conditions directly. In this paper, we developed a model to simulate VES acid leakoff. The model consists of two parts: the acid invaded zone and the compressed zone. Coupling of the two zones forms the VES acid leakoff model. In the invaded zone, we built a VES wormhole model, which simulates acid flow, acid-rock reaction, porosity variation, and acid viscosity variation. The VES wormhole model predicts the pressure field, the flow field, acid concentration distribution, cation concentration distribution, VES concentration distribution, and viscosity distribution. For the viscosity variation due to acid-rock reaction, we use a correlation of viscosity as a function of pH, temperature, cation concentration, VES concentration, and shear rate based on experiment results. With the model, by extensive numerical simulation, we analyzed wormhole progation behavior under VES acid flooding and put forth the mechanism of VES acid leakoff reduction. The study shows that wormholing and viscosifying have competitive effect on leakoff. Wormholing decreases flow resistance, while the viscosifying and the increase of the width of spent acid zone raise flow resistance. Wormholes have fewer branches under VES acid compared to regular acid. For reservoirs with small compressibility, for example oil reservoirs, VES acid has relatively small effect on leakoff because compressibility has dominant effect on leakoff ; while for reservoirs with large compressibility, for example gas reservoirs, VES acid has a significant contribution to leakoff reduction because viscosity has a dominant effect on leakoff.