Unsteady fluid flows in a three-dimensional porous structure consisting of spherical bodies at relatively high Reynolds numbers are numerically investigated by using the lattice Boltzmann method with the fifteen-velocity model. When the Reynolds number, defined by the superficial velocity and the equivalent diameter of the body, is higher than about 80, unsteady vortices appear behind the bodies and the flow fields become time-dependent. The characteristics of the transition from laminar to turbulent flow are studied by calculating the velocity fluctuations, the power spectra, and the turbulence intensity at three different points in the structure. It is found that the Reynolds numbers where the velocity fluctuation begins and the transition from laminar to turbulent flow occurs depend on the positions in the structure.