This paper addresses the estimation of the lateral velocity using a Frequency-Modulated Continuous-Wave (FMCW) radar. Usually lateral velocity estimation is performed by evaluating the range information during multiple sweeps by means of a tracking algorithm. Another approach is to use the Doppler frequency shift during one chirp of an FMCW waveform in conjunction with the instantaneous aspect angle of the target. But all these algorithms ignore the phase information between nearby chirps. In this contribution an estimator based on the phasing between adjacent sweeps is presented using contrast optimization in combination with the discrete polynomial-phase transform in order to reduce the computational demands of the proposed estimator. This approach makes it suitable for real-time implementation with state of the art technology.