The critical behaviour of fully directed Levy flight on a square lattice is studied using the Monte Carlo method. The obtained critical exponents nu , nu /sub /// and nu _{perpendicular to} are independent of the parameter u. This seems to be interesting compared with the Levy flight previously discussed by Halley and Nakanishi (1985), for which nu depends on u in addition to d. It also indicates that the introduction of the direction plays a dominant role in directed Levy flight just as in directed SAW, with nu , nu /sub /// and nu _{perpendicular to} independent of d.