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.
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