The frequency offset estimation method for chirp signal has the problem of limited resolution and low estimation accuracy. A Frequency Offset Estimation based on Matched Filter Interpolation (MFI-FOE) method is proposed. Firstly, the received signal is filtering matched with the corresponding matching signal. Then, the peak value of the waveform at the output of the matched filter is searched. Finally, we calculate the relative deviation and interpolate between the peak and the left or right point of the immediately adjacent peak to obtain an accurate frequency offset estimation. The simulation results show that the signal-noise ratio threshold of MFI-FOE method is reduced by 2~4 dB compared with the traditional frequency offset estimation method, and the performance is stable in the whole range of relative frequency offset estimation. The Normalized Mean Square Error (NMSE) of the frequency offset estimation is closer to the Cramer-Rao Bound. Therefore, MFI-FOE method can significantly improve the accuracy of estimation and anti-noise ability, which verifies the effectiveness of the method.