MuOn-decay MEdium baseline NeuTrino beam experiment (MOMENT) is a next-generation accelerator neutrino experiment, which can be used to probe new physics beyond Standard Model. We try to simulate neutrino oscillations confronting with Charged-Current and Non-Standard neutrino Interactions(CC-NSIs) at MOMENT. These NSIs could alter neutrino production and detection processes and interfere with neutrino oscillation channels. We separate a perturbative discussion of oscillation channels at near and far detectors, and analyze parameter correlations with the impact of CC-NSIs. Taking $\delta_{cp}$ and $\theta_{23}$ as an example, we find that CC-NSIs can induce bias in precision measurements of standard oscillation parameters. In addition, a combination of near and far detectors using Gd-doped water cherenkov technology at MOMENT is able to provide good constraints of CC-NSIs happening to the neutrino production and detection processes.