  Motivated by the recently measured muon's anomalous magnetic moment
$a_{\mu}$, we examine the supersymmetry contribution to $a_{\mu}$ in various
mediation models of supersymmetry breaking which lead to predictive flavor
conserving soft parameters at high energy scale. The studied models include
dilaton/modulus-mediated models in heterotic string/$M$ theory, gauge-mediated
model, no-scale or gaugino-mediated model, and also the minimal and deflected
anomaly-mediated models. For each model, the range of $a^{SUSY}_{\mu}$ allowed
by other experimental constraints, e.g. b --> s\gamma and the collider bounds
on superparticle masses, is obtained together with the corresponding parameter
region of the model. Gauge-mediated models with low messenger scale can give
any $a^{SUSY}_{\mu}$ within the $2\sigma$ bound. In many other models, b -->
s\gamma favors $a^{SUSY}_{\mu}$ smaller than either the $-1\sigma$ value
($26\times 10^{-10}$) or the central value ($42\times 10^{-10}$).
