Piezoelectricity is a unique material property that converts mechanical energy into electricity or vice versa. Starting from the group-III monochalcogenide monolayers, we design a series of derivative Janus structures for piezoelectric materials, including Ga2SSe, Ga2STe, Ga2SeTe, In2SSe, In2STe, In2SeTe, GaInS2, GaInSe2, and GaInTe2. Our first-principles calculations show that these Janus structures are thermodynamically and dynamically stable. They have a bandgap in the range of 0.89-2.03 eV, lower than those of the perfect monolayers, and Ga2STe, Ga2SeTe, In2STe, and In2SeTe monolayers are direct gap semiconductors. They possess piezoelectric coefficients up to 8.47 pm/V, over four times the maximum value obtained in perfect group-III monochalcogenide monolayers. Moreover, the broken mirror symmetry of these Janus structures induces out-of-plane dipolar polarization, yielding additional out-of-plane piezoelectric coefficients of 0.07-0.46 pm/V. The enhanced piezoelectric properties enable the development of these novel two-dimensional materials for piezoelectric sensors and nanogenerators.