  A search for an axion-like particle with 2.7 billion $\psi(3686)$ events
collected by the BESIII detector is presented. No significant signal is
observed, and the upper limits on the branching fraction of
$J/\psi\rightarrow\gamma a$ and the ALP-photon coupling constant
$g_{a\gamma\gamma}$ are set at the 95% confidence level in the mass range of
$0.165\leq m_a\leq 2.84$ GeV/$c^2$. The limits on $B(J/\psi\rightarrow\gamma
a)$ range from $8.3\times10^{-8}$ to $1.8\times10^{-6}$ over the search region,
and the constraints on the ALP-photon coupling are the most stringent to date
for $0.165\leq m_a\leq 1.468$ GeV/$c^2$.
