The mutual controls of ferroelectricity and magnetism are stepping towards practical applications proposed for quite a few promising devices in which multiferroic thin films are involved. Although ferroelectricity stemming from specific spiral spin ordering has been reported in highly distorted bulk perovskite manganites, the existence of magnetically induced ferroelectricity in the corresponding thin films remains an unresolved issue, which unfortunately halts this step. In this work, we report magnetically induced electric polarization and its remarkable response to magnetic field (an enhancement of ?800% upon a field of 2 Tesla at 2 K) in DyMnO3 thin films grown on Nb-SrTiO3 substrates. Accompanying with the large polarization enhancement, the ferroelectric coercivity corresponding to the magnetic chirality switching field is significantly increased. A picture based on coupled multicomponent magnetic structures is proposed to understand these features. Moreover, different magnetic anisotropy related to strain-suppressed GdFeO 3-type distortion and Jahn-Teller effect is identified in the films.