The effect of low-dose-rate exposure to ionizing radiation on cancer risk is a major issue associated with radiation protection. Tissue stem cells are regarded as one of the targets of radiation-induced carcinogenesis. However, it is hypothesized that the effect of radiation may be reduced if damaged stem cells are eliminated via stem cell competition between damaged and intact stem cells. This would be particularly effective under very low-dose-rate conditions, in which only a few stem cells in a stem cell pool may be affected by radiation. Following this hypothesis, we constructed a simple mathematical model to discuss the influence of stem cell competition attenuating the accumulation of damaged cells under very low-dose-rate conditions. In this model, a constant number of cells were introduced into a cell pool, and the numbers of intact and damaged cells were calculated via transition and turnover events. A transition event emulates radiation dose, whereby an intact cell is changed into a damaged cell with a given probability. On the other hand, a turnover event expresses cell competition, where reproduction and elimination of cells occur depending on the properties of cells. Under very low-dose-rate conditions, this model showed that radiation damage to the stem cell pool was strongly suppressed when the damaged cells were less reproductive and tended to be eliminated compared to the intact cells. Furthermore, the size of the stem cell pool was positively correlated with reduction in radiation damage.