There are some original nonmagnetic point defects in the BaF₂ crystallite powder, such as interstitial and vacant F^- which can become paramagnetic centers by γ-ray-irradiation at room temperature. After γ-ray irradiation the paramagnetic point defects V_k, H, F and M centers, have been observed in the sample with experiment of electron spin resonance (ESR). Frenkel exciton, a nonmagnetic point defect, can also be induced by the γ-ray irradiation in the sample at room temperature, the existence of the Frenkel exciton is affirmed by an anomalous change of the ESR signal of V_k center with temperature. The signals of the ESR of the H, F and M centers weaken and vanish with the temperature increasing monotonously. But the ESR signal of the V_k enhances when the temperature goes up about 127°C, then weakens and vanishes. An increase in the Vk center follows an annihilation of the Frenkel exciton with heating.