We report an intensive study on negative magnetization under zero-field-cooled (ZFC) mode in YMn0.5Cr0.5O3 polycrystalline samples. It has been found that the magnetization reversal in ZFC measurements is strongly related to a giant coercivity of the oxide. The giant coercivity may result from the cooperative effect of magnetocrystalline anisotropy and the Dzyaloshinsky-Moriya interaction, especially at temperatures below 10 K. By fitting the high-temperature paramagnetic data under nominal zero field, the value of the trapped field in a superconducting magnet has been derived to be around several Oe, which further demonstrates that the negative ZFC magnetization is an artifact caused by negative trapped field in combination with the giant coercivity. Consequently, we suggest that one has to be cautious of trapped field in superconducting magnets in understanding negative ZFC magnetization, especially in "hard" magnetic samples.