This article presents a numerical study of inclined pneumatic conveying using the combination of the discrete element model (DEM) for the particles and computational fluid dynamics (CFD) for the gas. In the numerical model, periodic boundary conditions (PBCs) are applied to both gas and particles in the conveying direction for computational efficiency. The validity of the model is first examined by comparing the calculated and measured results in terms of solids flow rate and gas pressure drop during pneumatic conveying with a pipeline inclination angle varying from 0 degrees to 90 degrees. On this basis, the effects of inclination angle, solids flow rate, and gas velocity on gas pressure are quantified. The contributions of different forces including the particle-wall friction force, particle gravitational force, and fluid-wall friction force to the pressure drop are examined. Finally, the energy dissipation as a result of interactions between particles, between particles and wall, between particles and fluid, between fluids, and between fluid and wall is studied in detail. The results show that the energy loss during steady-state inclined pneumatic conveying can mainly be attributed to particle-fluid energy dissipation, gravitational potential energy, particle-wall friction energy dissipation, and fluid-wall viscous energy dissipation. These energy dissipations vary significantly with inclination angle and flow regime.