Relationship between magnetic ordering and ferroelectric polarization switching in YMnO3 epitaxial thin film was investigated. It was found that Néel point of the YMnO3 film is below 80 K, which is consistent with that of YMnO3 single crystal by neutron diffraction. From temperature dependence of the polarization-electric field hysteresis loops and the dielectric permittivity-voltage characteristics, ferroelectric polarization switching behavior was investigated from 300 to 10 K in detail. The ferroelectric polarization switching behavior accords with Ishibashi-Orihara’s theory. Moreover, it was found that the dielectric permittivity under bias electric field have a anomaly below 80 K and the nucleation density for the ferroelectric polarization switching decreases below 130 K, which is higher than 80K.