Large-aperture coprime arrays (CAs) are expected to achieve higher sensing resolution than conventional dense arrays (DAs), yet with lower hardware and energy cost. However, existing CA far-field localization methods cannot be directly applied to near-field scenarios due to channel model mismatch. To address this issue, in this paper, we propose an efficient near-field localization method for CAs. Specifically, we first construct an effective covariance matrix, which allows to decouple the target angle-and-range estimation. Then, a customized two-phase multiple signal classification (MUSIC) algorithm for CAs is proposed, which first detects all possible targets' angles by using an angular-domain MUSIC algorithm, followed by the second phase to resolve the true targets' angles and ranges by devising a range-domain MUSIC algorithm. Finally, we show that the proposed method is able to locate more targets than the subarray-based method as well as achieve lower root mean square error (RMSE) than DAs.