The glueball spectrum is studied using an improved gluonic action on asymmetric lattices in the pure SU(3) lattice gauge theory. The smallest spatial lattice spacing is about 0.08 fm which makes the extrapolation to the ontinuum limit more reliable. Converting our lattice results to physical units using the scale set by the static quark potential, we obtain the following results for the glueball masses: MG(0++) -= 1730(90) MeV for the scalarglueball and MG(2++) = 2400(95) MeV for the tensor glueball.