Breathing and heartbeat are critical vital signs which reflect the health status of human beings. Aiming to accurately measure the vital sign in short time window, a novel signal processing method for Doppler radar vital sign detection is proposed. Firstly, a two-step I/Q mismatch correction method which, respectively, estimates the time invariant phase imbalance and gain ratio of I/Q channels in the calibration step and the direct-current offsets during normal operation has been proposed. By decreasing the number of estimation parameters from 5 to 2, the parameters can be effectively estimated with data distributed over shorter arc lengths. Then, to solve the discontinuity occurred in arctangent demodulation, the displacement information of chest movement is extracted from the calibrated I/Q signals by extended differentiate and cross multiply algorithm. Finally, instead of Fourier transform-based methods which require long time windows to guarantee sufficient frequency resolution, the optimal parameters of respiration and heartbeat are found by the intelligent search of the differential evolution algorithm. The experimental results show that the proposed method can accurately measure respiratory rate and heartbeat rate with a short time window. For the 8 s time window, the mean absolute errors of respiration and heartbeat were 0.52 bpm and 0.79 bpm, respectively, demonstrating its promise in real-time applications.