Acoustic velocity vectors are important for human's localization of sound at low frequencies. This paper proposes a sound field reproduction algorithm, which matches the acoustic velocity vectors in a circular listening area. In previous work, acoustic velocity vectors are matched either at sweet spots or on the boundary of the listening area. Methods based on sweet spots experience performance degradation when the listener moves away from sweet spots, whereas measuring the acoustic velocity vectors on the boundary requires complicated measurement setup. This paper proposes the radial independent cylindrical harmonic coefficients of the acoustic velocity vectors (CHV-indR coefficients) in the circular listening area, which are calculated from the cylindrical harmonic coefficients of the pressure in the circular listening area by using the sound field translation formula. The cylindrical harmonic coefficients of the pressure can be measured by a circular microphone array, which can be bought off-the-shelf. By matching the CHV-indR coefficients, the acoustic velocity vectors are reproduced throughout the listening area. Simulations show that at low frequencies, where the acoustic velocity vectors are the dominant factor for localization, the proposed reproduction method based on matching the CHV-indR coefficients results in higher accuracy in reproduced acoustic velocity vectors when compared with traditional method based on matching the cylindrical harmonic coefficients of the pressure.