In this study, we intend to inquire of how the temporal variation and spatial distribution of magnetic helicity injection in a CME-producing solar active region are related to the CME occurrence. We therefore investigate long-term (a few days) variation of magnetic helicity injection in the active region NOAA 9236 which produced multiple CME events. As a result, it is found that a noticeable increase in helicity of negative sign was first made for the first ~1.5 days and then 6 CMEs occurred while the relatively more injection of oppositely signed (positive) helicity was taking place for the next ~2 days. Afterwards, 2 CMEs in the region occurred while a more negative helicity is being injected again compared to a positive helicity. In addition, from helicity flux density maps, we found that the CMEs originated from this active region seem to be involved with the interaction of two magnetic field systems characterized by opposite signs of helicity.