Barium fluoride (BaF2) crystal is known as the fastest scintillation crystal, which has a wide application prospect in high energy physics, nuclear physics and nuclear medicine. It is very important to suppress the slow luminescence component of BaF2 crystal for its engineering application. BaF2 crystals with high Y3+ doping concentration 5%, 8%, 10% (mole fraction) were prepared by Bridgman method, and the codoped BaF2 fast response scintillation crystals were prepared by codoping Y3+ with alkali metal ions (Li+, Na+) to form charge compensation to eliminate the generation of interstitial F-. Then, based on the optimized 5 ns and 2 500 ns time gate width measurement methods, the effects of Y3+ doping concentration and the codoping concentration of Y3+ and alkali metal ions (Li+, Na+) on the fast/slow component ratio of BaF2 scintillation crystal were studied. The results show that the optical quality of the high concentration Y3+ doped BaF2 crystals is excellent, and the transmittance at 220 nm and 300 nm is higher than 90% and 92%, respectively. With the increase of Y3+ doping concentration from 0 to 10%， the slow luminescence component of BaF2 crystal decrease significantly, and the fast/slow component ratio increase from 0.15 to 1.21. The slow luminescence component of the grown Y3+/Li+ and Y3+/Na+ codoped BaF2 crystals are further decrease compared with that of the Y3+ doped BaF2 crystals, and the highest fast/slow component ratios obtained are 1.63 and 1.61, respectively. The codoped BaF2 fast response scintillation crystal is expected to be applied in the frontier experiments of high energy physics and nuclear physics.