The curvilinear‐grid finite‐difference method (FDM), which uses curvilinear coordinates to discretize the nonplanar interface geometry, is extended to simulate acoustic and seismic‐wave propagation across the fluid–solid interface at the sea bottom. The coupled acoustic velocity‐pressure and elastic velocity‐stress formulation that governs wave propagation in seawater and solid earth is expressed in curvilinear coordinates. The formulation is solved on a collocated grid by alternative applications of forward and backward MacCormack finite difference within a fourth‐order Runge–Kutta temporal integral scheme. The shape of a fluid–solid interface is discretized by a curvilinear grid to enable a good fit with the topographic interface. This good fit can obtain a higher numerical accuracy than the staircase approximation in the conventional FDM. The challenge is to correctly implement the fluid–solid interface condition, which involves the continuity of tractions and the normal component of the particle velocity, and the discontinuity (slipping) of the tangent component of the particle velocity. The fluid–solid interface condition is derived for curvilinear coordinates and explicitly implemented by a domain‐decomposition technique, which splits a grid point on the fluid–solid interface into one grid point for the fluid wavefield and another one for the solid wavefield. Although the conventional FDM that uses effective media parameters near the fluid–solid interface to implicitly approach the boundary condition conflicts with the fluid–solid interface condition. We verify the curvilinear‐grid FDM by conducting numerical simulations on several different models and compare the proposed numerical solutions with independent solutions that are calculated by the Luco‐Apsel‐Chen generalized reflection/transmission method and spectral‐element method. Besides, the effects of a nonplanar fluid–solid interface and fluid layer on wavefield propagation are also investigated in a realistic seafloor bottom model. The proposed algorithm is a promising tool for wavefield propagation in heterogeneous media with a nonplanar fluid–solid interface.