  Using a sample of $58\times 10^6$ $J/\psi$ events collected with the BESII
detector, radiative decays $J/\psi\to\gamma\gamma V$, where $V=\rho$ or $\phi$,
are studied. A resonance around 1420 MeV/c$^2$ (X(1424)) is observed in the
$\gamma\rho$ mass spectrum. Its mass and width are measured to be $1424\pm
10(stat)\pm 11(sys)$ MeV/c$^2$ and $ 101.0\pm 8.8 \pm 8.8$ MeV/c$^2$,
respectively, and its branching ratio $B(J/\psi\to \gamma X(1424)\to \gamma
\gamma \rho)$ is determined to be $(1.07\pm0.17 \pm 0.11)\times 10^{-4}$. A
search for $X(1424)\to \gamma\phi$ yields a 95% C.L. upper limit $B(J/\psi\to
\gamma X(1424)\to \gamma\gamma \phi) < 0.82 \times 10^{-4}$.
