The FCMOM (finite size domain complete set of trial functions method of moments) is an efficient and accurate numerical technique to solve monovariate and bivariate population balance equations. It was previously formulated for homogeneous systems. In this paper, the FCMOM approach is extended to solve monovariate population balance equations for inhomogeneous (spatially not uniform) systems. In the FCMOM, the method of moments is formulated in a finite domain of the internal coordinates and the particle size distribution function is represented as a truncated series expansion by a complete system of orthonormal functions The FCMOM is extended to inhomogeneous systems assuming that the particle-phase convective velocity is independent of the internal variables (particle size). The method is illustrated by applications to particle diffusion and to particle convection In the case of particle convection, a gas-solid dilute flow in a pipe was simulated and the FCMOM equations were coupled with the governing equations (mass and momentum balances) of the gas phase