Using the near-IR spectroscopy of the MOSFIRE Deep Evolution Field (MOSDEF) survey, we investigate the role of local environment in the gas-phase metallicity of galaxies. The local environment measurements are derived from accurate and uniformly calculated photometric redshifts with wellcalibrated probability distributions. Based on rest-frame optical emission lines, [NII]λ6584 and Hα, we measure gas-phase oxygen abundance of 167 galaxies at 1.37 ≤ z ≤ 1.7 and 303 galaxies at 2.09 ≤ z ≤ 2.61, located in diverse environments. We find that at z ∼ 1.5, the average metallicity of galaxies in overdensities with M * ∼ 10 9.8 M , 10 10.2 M and 10 10.8 M is higher relative to their field counterparts by 0.094 ± 0.051, 0.068 ± 0.028 and 0.052 ± 0.043 dex, respectively. However, this metallicity enhancement does not exist at higher redshift, z ∼ 2.3, where, compared to the field galaxies, we find 0.056 ± 0.043, 0.056 ± 0.028 and 0.096 ± 0.034 dex lower metallicity for galaxies in overdense environments with M * ∼ 10 9.8 M , 10 10.2 M and 10 10.7 M , respectively. Our results suggest that, at 1.37 ≤ z ≤ 2.61, the variation of mass-metallicity relation with local environment is small (< 0.1dex), and reverses at z ∼ 2. Our results support the hypothesis that, at the early stages of cluster formation, owing to efficient gas cooling, galaxies residing in overdensities host a higher fraction of pristine gas with prominent primordial gas accretion, which lowers their gas-phase metallicity compared to their coeval field galaxies. However, as the Universe evolves to lower redshifts (z 2), the shock-heated gas in overdensities cannot cool down efficiently, and galaxies become metal-rich rapidly due to the suppression of pristine gas inflow and re-accretion of metal-enriched outflows in overdensities.