We have performed a numerical simulation of coalescence of spinning binary neutron stars with large approaching velocity using a Newtonian hydrodynamics code including radiation reaction by gravitational waves in order to examine the effect of plunging orbit of each neutron star. We found that at first two neutron stars coalesce like a head on collision and then the coalescing object becomes the double core structure. This structure is kept for a considerably long time because the angular momentum is not lost so efficiently. The wave pattern of gravitational waves is also at first similar to that in the case of the head on collision and then similar to that in the coalescence of spinning neutron stars with no plunging velocity. The maximum amplitude of gravitational waves is 3.6 x 10(-21) for a hypothetical event at the distance of 10 Mpc.