  We study the muon anomalous magnetic moment $(g-2)_{\mu}$ in the context of
the reduced minimal 3-3-1 model recently proposed in the literature. In
particular, its spectrum contains a doubly charged scalar ($H^{\pm \pm}$) and
gauge boson ($U^{\pm \pm}$), new singly charged vectors ($V^{\pm}$) and a
$Z^{\prime}$ boson, each of which might give a sizeable contribution to the
$(g-2)_{\mu}$. We compute the 1-loop contributions from all these new particles
to the $(g-2)_{\mu}$. We conclude that the doubly charged vector boson provides
the dominant contribution, and by comparing our results with the experimental
constraints we derive an expected value for the scale of $SU(3)_L\otimes
U(1)_N$ symmetry breaking $v_{\chi} \sim 2$ TeV. We also note that, if the
discrepancy in the anomalous moment is resolved in the future without this
model then the constraints will tighten to requiring $v_\chi > 2.7$ TeV with
current precision, and will entirely rule out the model if the expected
precision is achieved by the future experiment at Fermilab.
