  We discuss the short-time behavior of the majority vote dynamics on
scale-free networks at the critical threshold. We introduce a heterogeneous
mean-field theory on the critical short-time behavior of the majority-vote
model on scale-free networks. In addition, we also compare the heterogeneous
mean-field predictions with extensive Monte Carlo simulations of the short-time
dependencies of the order parameter and the susceptibility. We obtained a
closed expression for the dynamical exponent $z$ and the time correlation
exponent $\nu_\parallel$. Short-time scaling is compatible with a non-universal
critical behavior for $5/2 < \gamma < 7/2$, and for $\gamma \geq 7/2$, we have
the mean-field Ising criticality with additional logarithmic corrections for
$\gamma=7/2$, in the same way as the stationary scaling.
