Vortex lattices of four fold symmetric superconductors are studied numerically on the basis of the quasiclassical theory. The four fold symmetric anisotropy of the Fermi velocity or the superconducting gap function causes the vortex lattice transformation. The transformation as observed in LuNi2B2C could be understood with the four fold symmetric anisotropy. We show the temperature and field phase diagram for four fold symmetric superconductors and the spatial structures of the pair potential and zero energy states in the case of the stable square vortex lattice at the low field. (C) 2003 Elsevier Science B.V. All rights reserved.