Acoustic sound generated by the head-on and oblique collisions of two vortex rings with equal strength is investigated by a direct numerical simulation (DNS). The three-dimensional, unsteady, compressible Navier-Stokes equations are solved by a finite difference method over the whole domain from near-vortical field to far-acoustic field. Vortex collision for three initial angles are investigated, and the effects of the collision angle on the vortex motion and characteristic features of the acoustic sound are clarified. In any of the three cases, quadrupolar nature is predominant, but the directivities of the sound pressure are different among the three collision angles. For the oblique collisions, octupolar component appears in addition to the quadrupolar component, and this octupolar component becomes larger with decreasing collision angle.