  The prompt emission of most gamma-ray bursts (GRBs) typically exhibits a
non-thermal Band component. The synchrotron radiation in the popular internal
shock model is generally put forward to explain such a non-thermal component.
However, the low-energy photon index $\alpha \sim -1.5$ predicted by the
synchrotron radiation is inconsistent with the observed value $\alpha \sim -1$.
Here, we investigate the evolution of a magnetic field during propagation of
internal shocks within an ultrarelativistic outflow, and revisit the fast
cooling of shock-accelerated electrons via synchrotron radiation for this
evolutional magnetic field. We find that the magnetic field is first nearly
constant and then decays as $B'\propto t^{-1}$, which leads to a reasonable
range of the low-energy photon index, $-3/2 < \alpha < -2/3$. In addition, if a
rising electron injection rate during a GRB is introduced, we find that
$\alpha$ reaches $-2/3$ more easily. We thus fit the prompt emission spectra of
GRB 080916c and GRB~080825c.
