Time-reversal imaging with the MUltiple SIgnal Classification (MUSIC) method for the location of point targets was first proposed by Devaney et al. In this paper, a recursive time-reversal MUSIC algorithm is proposed. The considered approach is based on the Recursively Applied and Projected (RAP) MUSIC which was first introduced for magnetoencephalographic (MEG) data processing. The main goal of this contribution is to test and study a time-reversal RAP-MUSIC approach for target location and imaging.