  Dark sector may exist and interact with Standard Model (SM) through the
$U(1)$ kinetic mixing. Through this portal-type interaction, dark photon from
dark sector couples to SM fermions, and may explain the discrepancy between
experimental data and SM calculations on muon anomalous magnetic moment, muon
$g-2$. However, current searches for dark photon impose stringent constraints
on the mixing parameter $\varepsilon$ for various dark photon masses, excluding
the favorite parameter space for muon $g-2$. In this paper, we study the case
where a global $U(1)$ in dark sector is spontaneously broken, resulting a light
pseudo-Goldstone, axion-like particle (ALP) $a$, which couples to dark photon
and SM photon, $g_{a\gamma\gamma'}$. Through this interaction, dark photon may
decay into photon and ALP when this channel is kinematically allowed. As a
result, the experimental constraints on dark photon change significantly, and
dark photon is able to explain the muon $g-2$ anomaly when its mass is heavier
than $10$ GeV.
