  The disagreement between the standard model prediction and the experimental
measurement of muon anomalous magnetic moment can be alleviated by invoking an
additional particle which is either a vector boson ($X_1$) or a scalar ($X_0$).
This new particle, with the mass $m_X \lesssim 2 m_\mu$, can be searched for in
the decay $J/\psi \to \mu^- \mu^+ X$, where $X$ is missing. Our numerical study
shows that the search is quite feasible at the BESIII experiment in the
parameter space allowed by muon $g-2$ measurements.
