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To avoid 2-D search, a two-stage algorithm for passively estimating the azimuth and range of a near-field source using an acoustic vector sensor is proposed. This algorithm utilizes two particle velocity channels to estimate the azimuth, and then combines the pressure channel to estimate the range. The Cramé r-Rao bound (CRB) on the estimation errors of the source azimuth is derived. Compared with the traditional method and CRB, The proposed algorithm is computationally efficient and has the similar performance with 2-D MUSIC algorithm. Simulation results are provided to demonstrate the high-efficient quality of this method.