Real-time angle measurement of missiles is as important as range measurement for precision strike in modern wars and fuse using linear frequency modulation (LFM) system has been equipped widely due to its good range resolution. However, angle measurement of fuse using LFM system hasn’t been realized. In order to achieve the accurate and rapid measurement of angle, this paper firstly derives the relationship between angle and phase of beat signal in the LFM system. Secondly, an arithmetic called AapFFT-CZT is proposed by sampling and inserting zeros based on all-phase Fourier Transform (apFFT) and Chirp Z Transform (CZT). Compared with traditional Fast Fourier Transform (FFT), AapFFT-CZT has higher accuracy and better anti-noise performance when used to measure angle. Thirdly, angle measurement utilizing AapFFT-CZT is performed successfully on single core of TMS320C6678. When there is no noise, accuracy of angle measurement is within 0.01°. When there is Gaussian white noise, accuracy is still within 0.25°. Last but not least, fast and parallel measurement on multiple cores is achieved. The results show that clocks consumed when using multiple cores is just 57% of clocks consumed when using single core. Therefore, angle can be measured accurately and quickly based on C6678 multi-core DSPs.