  The radiative decay of $J/\psi$ into a pure gauge tensor glueball is studied
in the quenched lattice QCD formalism. With two anisotropic lattices, the
mutlipole amplitudes E_1(0), M_2(0) and E_3(0) are obtained to be
0.114(12)(6)GeV, -0.011(5)(1)GeV, and 0.023(8)(1)GeV, respectively. The first
error comes from the statistics, the Q^2 interpolation, and the continuum
extrapolation, while the second is due to the uncertainty of the scale
parameter r_0^{-1}=410(20) MeV. Thus the partial decay width
$\Gamma(J/\psi\rightarrow \gamma G_{2^{++}})$ is estimated to be 1.01(22)(10)
keV which corresponds to a large branch ratio 1.1(2)(1)x10^{-2}. The
phenomenological implication of this result is also discussed.
