In underwater explosion simulations, the accuracy is critically affected by numerical diffusion and the quality of the computational grid. An enhanced interface-sharpening algorithm, based on the five-equation model and an anti-diffusion source term, is proposed to simulate the strongly compressible multiphase flow with an arbitrary number of phases in underwater explosions. To enhance the precision of interface and maintain computational stability on nonuniform and unstructured grids, an adaptive factor algorithm and a continuous interface capture function are developed. Furthermore, a redesigned fractional step method incorporating a special iteration stop criteria is proposed to solve the volume fraction equation. A pressure–density cutoff model is used to calculate the mixture density at the saturation pressure to account for the effect of cavitation. The quadratic monotone upstream-centered scheme for conservation laws reconstruction scheme and the improved advection upstream splitting method (AUSM+-up) flux scheme are also adopted to compute the flux across the grid interfaces. The overall computational framework is constructed upon a density-based explicit finite volume method. To assess the accuracy and robustness of the proposed numerical model, four representative test cases were chosen. The results reveal that the model refines the phase interface, adeptly capturing the complexities inherent in underwater explosion scenarios with both precision and efficiency across a diverse array of conditions.