In the lower part of a circulating fluidized bed (CFB) riser, the solids are accelerated towards a fully developed state. Understanding on hydrodynamic behaviors of solids in the acceleration zone is particularly important due to the high solids holdup and long solids residence time as well as the dramatic variations in solids concentration, velocity and pressure drop within this zone. While many studies on the axial solid flow structure have been reported, almost all of them are based on the assumption of fully developed flows where the pressure gradients are completely converted to the axial distribution of solids concentrations. However, as shown by our model predictions, the pressure drop due to the solid acceleration in the acceleration zone is far more than negligible, compared to the pressure drop for the solids concentration. In addition, the pressure drop due to energy dissipation from inter-particle collisions, particle-wall frictions, and gas-solids friction also plays an important role when solids concentration is high. In this paper, a one-dimensional model has been developed to characterize the pressure drop partitions among solids concentration, solids acceleration, and energy loss in the acceleration zone in a CFB riser. The axial distributions of solid velocity and solid concentration are obtained by solving the equations. Consequently effects of solids acceleration and energy loss on the axial distributions of solids velocity and concentration are illustrated.