Densely occupied spaces (e.g., classrooms) are generally over-crowded and pose a high risk of cross-infection during the pandemic of COVID-19. Among various ventilation systems, impinging jet ventilation (IJV) system might be promising for such spaces. However, the exhaust location of the IJV system used for densely occupied classrooms is unclear. This study aims to investigate the effects of exhaust location on the removal of exhaled contaminants in a classroom (15 × 7 × 5 m3) occupied by 50 students. Exhaled contaminants are modeled by a tracer gas released at the top of each manikin. The reference case has three exhausts evenly distributed in the ceiling. The results indicate that: a) a recirculation airflow entraining exhaled contaminants exists above the occupied zone; b) this recirculation air flow entrains contaminants and accumulates them at the upper part of the room near the diffuser; c) locating merely one exhaust on the same side of the supply diffuser leads to the best indoor air quality, i.e., it reduces the mean age of air from 278 s to 243 s, the mass fraction of CO2 from 753 ppm to 726 ppm, and the concentration of tracer gas from 305 ppm to 266 ppm; d) this layout still performs the best when the supply velocity drops to 0.5 m/s. It is worth noting that the proposed layout has fewer exhausts than the reference case but performs better. These results conclude that the exhaust for large spaces is not evenly distributed but depends on the indoor airflow pattern: the key is locating the exhaust near the region with high contaminant concentration. Factors determining the recirculation airflow are suggested to be further studied.