We present a space-time model of the collision of two homogeneous, plane impulsive gravitational waves (each having a delta function profile propagating in a vacuum before collision and for which the post-collision space-time has constant curvature. The profiles of the incomong waves are k*\delta(u) and l*\delta(v) where k,l are real constants and u=0, v=0 are the intersecting null hypersurfaces. The cosmological constant \Lambda in the post-collision region of the space-time is given by \Lambda = -6*k*l.