  The discrepancy between the measured value and the Standard Model prediction
of the muon anomalous magnetic moment is one of the most important issues in
the particle physics. It is known that introducing a mediator boson X with the
$\mu \tau$ lepton flavor violating (LFV) couplings is one good solution to
explain the discrepancy, due to the $\tau$ mass enhancement in the one-loop
correction. In this paper, we study the signal of this model, i.e. the
same-sign leptons, in the Belle II experiment, assuming the flavor-diagonal
couplings are suppressed. We show that the Belle II experiment is highly
sensitive to the scenario in the mediator mass range of ${\cal O}(1-10)$~GeV,
using the $e^+e^- \to \mu^\pm\tau^\mp X \to\mu^\pm \mu^\pm \tau^\mp \tau^\mp$
process induced by the $X$.
