Scalar and tensor glueball spectrum is studied using an improved gluonic ac
tion on asymmetric lattices in the pure SU(3) gauge theory. The smallest sp
atial lattice spacing is about 0.08 fm which makes the extrapolation to the
continuum limit more reliable. In particular, attention is paid to the sca
lar glueball mass which is known to have problems in the extrapolation. Con
verting our lattice results to physical units using the scale set by the st
atic quark potential, we obtain the following results for the glueball mass
es: MG(0(++)) = 1730(90)MeV for the scalar glueball mass and M-G(2(++)) = 2
400(95)MeV for the tensor glueball.