The observed speeds of coronal mass ejections are often below the estimated Alfvén speed but above the sound speed for the background solar corona. This circumstance suggests that coronal mass ejections may form slow shocks in the corona. This paper presents a numerical simulation of the slow shock triggered by a coronal mass ejection, taking a coronal streamer with an equatorial current sheet as the background and a magnetic flux eruption at the base of the streamer as the driving mechanism. The results show that the current sheet has a significant influence on the structure of the shock wave. The slow shock occurs only on the outside of the current sheet and is gradually being transformed into a fast shock within the sheet. A fast magnetosonic wave exists in front of the slow shock, and it deflects the background magnetic field substantially and reduces the background density by more than 10% over there. The slow shock has a limited extent in latitude from the edge of the current sheet to ± 20° and has a concave upward shape.