  Recent investigations have shown that the extended main-sequence turnoffs
(eMSTOs) are a common feature of intermediate-age star clusters in the
Magellanic Clouds. The eMSTOs are also found in the color-magnitude diagram
(CMD) of young-age star clusters. The origin of the eMSTOs is still an open
question. Moreover, asteroseismology shows that the value of the overshooting
parameter $\delta_{\rm ov}$ of the convective core is not fixed for the stars
with an approximatelly equal mass. Thus the MSTO of star clusters may be
affected by the overshooting of the convective core (OVCC). We calculated the
effects of the OVCC with different $\delta_{\rm ov}$ on the MSTO of young- and
intermediate-age star clusters. \textbf{If $\delta_{\rm ov}$ varies between
stars in a cluster,} the observed eMSTOs of young- and intermediate-age star
clusters can be explained well by the effects. The equivalent age spreads of
MSTO caused by the OVCC are related to the age of star clusters and are in good
agreement with observed results of many clusters. Moreover, the observed eMSTOs
of NGC 1856 are reproduced by the coeval populations with different
$\delta_{\rm ov}$. The eMSTOs of star clusters may be relevant to the effects
of the OVCC. The effects of the OVCC \textbf{are similar to that of rotation in
some respects. But the effects cannot result in a significant split of main
sequence of young star clusters at $m_{U}\lesssim 21$.} The presence of a rapid
rotation can make the split of main sequence of young star clusters more
significant.
