In this paper, we study the flow through a corrugated channel filled with a fluid-saturated sparsely packed porous medium. The porous medium flow is described by the Darcy-Lapwood-Brinkman system taking into account the Brinkman extension of the Darcy law and the flow inertia. We assume the periodicity of the roughness in the longitudinal direction and that the flow is governed by the prescribed pressure drop between the edges of the channel. Introducing average boundary roughness as the small parameter, we propose a higher-order correction of the Darcy-Brinkman filtration velocity via asymptotic analysis.