Abstract: Fractional Fourier transform (FrFT) is often used to analyze the linear frequency modulation (LFM) signal in active sonar. The relative velocity of the target can be estimated by searching the transform parameters. However, the parameter search process in this approach costs large amount of computations, and it is a heavy burden for small platforms with limited computation resource such as autonomous underwater vehicles. To reduce the computational complexity of FrFT, a method based on the quadratic phase transformation (QPT) is proposed to estimate the relative velocity. The close-form solution for the QPT of LFM signal with Doppler frequency shift is derived, which reveals the relationship between the spectrum broadening in the transformation domain and the Doppler frequency shift. In this method, the relative velocity is estimated by amplitude spectrum broadening after QPT, so transformation parameter scanning is avoided. The numerical results show that the proposed method decreases computational cost and provides precise velocity estimation of 1 m·s^-1.