$(TMTSF)_2BF_4$ containing non-centrosymmetric anions is well known to exhibit a metal insulator transition around 37 K by ordering of the anions with a $q_2$=(1/2, 1/2, 1/2) wave vector. We established pressure-temperature phase diagram of the $(TMTSF)_2BF_4$ compound and showed that it can belong to the general phase diagram of the $(TMTSF)_2X$ family. Application of hydrostatic pressure decreases the anion ordering transition temperature and the superconducting state is finally stabilized below 3.77 K under 7.7 kbar. Magnetoresistance measurement on the $(TMTSF)_2BF_4$ under 7.8 kbar is performed but neither the field-induced spin-density-wave state nor the rapid oscillation is observed up to 9 T.