It is common to adopt finite-element methods to solve solid mechanics problems and finite-volume methods for fluid dynamics computations. The use of different methods causes complication of the solution procedure for problems involving both fluids and solids. In this study, a partitioned approach based on the finite-volume method for dynamic fluid-structure interaction is presented. The method is formulated in a way suitable for an unstructured mesh with arbitrary grid geometry. The variables for the fluid are stored at the centroids of grid cells, whereas those for the solid at the grid nodes. The latter arrangement makes it more suitable for large structure deformation. After spatial discretization for the solid using the finite-volume approach, the resulting system of ordinary differential equations is solved implicitly using the dual-time-stepping scheme. As for the fluid calculation, a pressure-based algorithm is employed and the time step is advanced in a prediction-correction manner. The finite-volume method for the solid is assessed by calculating the deformation and dynamics of a cantilever under various loads. Good agreement with analytical solutions is obtained. Then, the solution procedure is applied to two cases with coupled fluid flow and structure dynamics. One is the flow over a vertical plate with one end fixed on the floor in a channel. The other is the flow over a cylinder with a plate attached to it on the lee side.