This study is undertaken to evaluate the relationship between the indoor $CO_2$ concentration and the local mean air-age in the lecture room with the occupants. We conducted the experiments to examine the indoor $CO_2$ concentration and the local mean air-age with respect to the supply airflow of the ventilation system and the discharge angle and air-flow of the system air conditioner. Through the experiments, we found out that indoor $CO_2$ concentrations calculated by the prediction equation of Seidel are about 350 ppm lower than those measured by the experiments. The indoor $CO_2$ concentration is not related with the air-flow and the discharge angle of the system air-conditioner, but with the ventilation airflow. From the numerical calculation, the indoor $CO_2$ concentration is not related with the ventilation effectiveness, but strongly with the local mean air-age. In case of our model, the indoor $CO_2$ concentration is likely to fall within the acceptable air quality when the local mean air-age is averagely predicted under 400 seconds.