We present a detailed simulation of the evolution of a moderately slow coronal mass ejection (CME; 800 km s−1 at 5 R☉, where R☉ is solar radii) in the lower solar corona (2-5 R☉). The configuration of the Sun's magnetic field is based on the MDI data for the solar surface during Carrington rotation 1922. The pre-CME background solar wind is generated using the Wang-Sheeley-Arge (WSA) model. To initiate a CME, we inserted a modified Titov-Demoulin flux rope in an active region near the solar equator using the Space Weather Modeling Framework (SWMF). After the initiation stage (within 2.5 R☉), the CME evolves at a nearly constant and slow acceleration of the order of 100 m s−2, which corresponds to an intermediate-acceleration CME. Detailed analysis of the pressures shows that the thermal pressure accounts for most of the acceleration of the CME. The magnetic pressure contributes to the acceleration early in the evolution and becomes negligible when the CME moves beyond ~3 R☉. We also present the evolution of the shock geometry near the nose of the CME, which shows that the shock is quasi parallel most of the time.