By numerically solving the two-dimensional semiconductor Bloch equation, this paper studies the high-order harmonic emission of a monolayer ZnO under the driving of co-rotating two-color circularly polarized laser pulses. By changing the relative phase between the fundamental frequency field and the second one, it is found that the harmonic intensity in the platform region can be significantly modulated. In the higher order, the harmonic intensity can be increased by about one order of magnitude. Through time-frequency analysis, it is demonstrated that the the emission trajectory of monolayer ZnO can be cotrolled by the relative phase, and the harmonic enhacment is caused by the second quantum trajectory with the higher emission probability. In addition, near-circularly polarized harmonics can be generated in the co-rotating two-color circularly polarized fields. With the change of the relative phase, the harmonics in the platform region can be altered from left-handed near-circularly polarization to right-handed one. Our results can obtain high-intensity harmonic radiation with an adjustable ellipticity, which provides an opportunity for the synthesis of circularly polarized attosecond pulses.