We theoretically demonstrate that the presence of Dzyaloshinskii-Moriya interaction (DMI) can lead to enhancement of the spin-motive force (SMF) arising due to field-induced ferromagnetic domain-wall motion. A SMF refers to an electric voltage induced by dynamical magnetic textures, which reflects the temporal and spatial variations of the magnetization. A DMI can introduce extra spatial rotation of the magnetization in the domain-wall region, which turns out to cause the enhancement of the SMF. We derive an expression for the SMF, and examine the field and DMI dependencies of the SMF. We find that the SMF can be amplified by up to an order of magnitude in the low field regime, where the external field is lower than the so-called Walker breakdown field.