Multi-frequency continuous waveform (MFCW) radar transmits a set of CW waveforms with different frequencies, which increase in a stepwise manner. This type of radar usually employs the spectrogram analysis of the baseband received echo signal, and therefore is capable of detecting and resolving two targets with different velocities but at the same range. However, this spectrogram approach renders difficulties in resolving two targets with the same velocity but at different ranges. We propose a new method that solves this problem by enabling the MFCW radar to estimate the velocity and range simultaneously using the local polynomial approximation (LPA). Namely, the range of a moving target is expanded using the Taylor series, attaining up to the second order terms, and the two Taylor coefficients, i.e., the range and velocities are estimated by the grid search. Simulation results show that the proposed LPA-based algorithm is able to resolve multiple targets with the same velocity satisfactorily.