We can obtain ranges and velocities of targets at same time by using a frequency modulated continuous wave (FMCW) Doppler radar. The two-dimensional Fourier transform is conventionally used as the two-dimensional (range and Doppler) spectral analysis on the received signal. The range resolution is determined by the bandwidth over which the FMCW signal is swept. The Doppler resolution is closely equal to the inverse of the coherent integration time (CIT). In this paper, we propose the spectral analysis method for FMCW Doppler radar using a Hopfield neural network, which can yield high-resolution spectra. In this method, the spectral analysis is reformulated as a minimisation problem of difference between the covariance matrixes calculated from observed data and theoretical values. This minimisation problem is mapped on the energy function of the Hopfield neural network and then letting the network converge to the minimum state of that energy function. High-resolution spectra are caused by the non-linear function of neurons and the global connectivity of the network. The performance of this method is evaluated by computer simulations and experimental results. Especially in Doppler resolution, the proposed method is demonstrated to be at least 3-times better than that processed by the conventional two-dimensional Fourier transform method. This high-resolution result contributes to shortening of the CIT and can improve time resolution of the FMCW Doppler radar system.