This paper proposes low-complexity super-resolution detection for range-vital Doppler estimation frequency-modulated continuous wave (FMCW) radar. In regards to vital radar, and in order to estimate joint range and vital Doppler information such as the human heartbeat and respiration, two-dimensional (2D) detection algorithms such as 2D-FFT (fast Fourier transform) and 2D-MUSIC (multiple signal classification) are required. However, due to the high complexity of 2D full-search algorithms, it is difficult to apply this process to low-cost vital FMCW systems. In this paper, we propose a method to estimate the range and vital Doppler parameters by using 1D-FFT and 1D-MUSIC algorithms, respectively. Among 1D-FFT outputs for range detection, we extract 1D-FFT results based solely on human target information with phase variation of respiration for each chirp; subsequently, the 1D-MUSIC algorithm is employed to obtain accurate vital Doppler results. By reducing the dimensions of the estimation algorithm from 2D to 1D, the computational burden is reduced. In order to verify the performance of the proposed algorithm, we compare the Monte Carlo simulation and root-mean-square error results. The simulation and experiment results show that the complexity of the proposed algorithm is significantly lower than that of an algorithm detecting signals in several regions.