We have performed numerical simulations of coalescence of binary neutron stars using a Newtonian hydrodynamics code including radiation reaction by gravitational waves. In order to examine the effect of spin, we start the simulations from two distinct types of the initial conditions. In the first case, to see the dependence of results on the initial separation of binary, a Roche solution of separation 27 km, each mass approximately 1.5 M. and each radius approximately 9 km, respectively, is given as the initial condition. We found that the evolution sequence and the wave form of gravitational waves are essentially the same as those in the previous simulations in which computations are started when two neutron stars just contact. In the second case, we include spin of each star with -OMEGA, where OMEGA is Keplerian angular velocity of orbital motion, which is required from the conservation of the circulation. We found that the wave pattern has high amplitude oscillation after coalescence contrary to the former case. This means that it will be possible to determine the spin of coalescing neutron stars from the observed wave form of gravitational waves. The maximum amplitude of gravitational waves is 3.4 x 10(-21) for a hypothetical event at the distance of 10 Mpc.