This work proposes a method for localizing a single near-field source using a moving array. Using a phase correction factor calculated from two sequences of selected data snapshots, we extend the array aperture and compute the initial estimates of the source's bearing and range from the extended data sets. With the initial estimates of bearing and range we construct a phase difference factor to modify the data sets into the ones as if they were collected by a stationary extended array. Finally the localization of the single near-field source is carried out by using a modified 2-D MUSIC with parameter refinement iterations on the modified data sets. Simulation results are presented to demonstrate the feasibility of the proposed method.