  We search for the di-photon decay of a light pseudoscalar axion-like
particle, $a$, in radiative $J/\psi$ decays, using 10 billion $J/\psi$ events
collected with the BESIII detector. We find no evidence of a signal and set
upper limits at the $95\%$ confidence level on the product branching fraction
$\mathcal{B}(J/\psi \to \gamma a) \times \mathcal{B}(a \to \gamma \gamma)$ and
the axion-like particle photon coupling constant $g_{a \gamma \gamma}$ in the
ranges of $(3.7-48.5) \times 10^{-8}$ and $(2.2 -101.8)\times 10^{-4}$
GeV$^{-1}$, respectively, for $0.18 \le m_a \le 2.85$ GeV/$c^2$. These are the
most stringent limits to date in this mass region.
