A under-damping second-order system model without excitation was proposed to measure the quality factor(Q factor) for a vacuum packaged microgyroscope. The model was analyzed theoretically and a time decay constant method was presented. Firstly, an initial displacement of the seismic mass was obtained by exciting the microgyroscope to implement a closed loop resonance with a Phase Locked Loop (PLL). By releasing the excitation signal, the vibration amplitude decay curve was then acquired through demodulating the vibrating displacement signal and was transferred to a computer by a Field Programming Gate Array(FPGA) hardware and Matlab GUI software simultaneously. Finally, the Q factor of the vacuum packaged microgyroscope was calculated by exponentially fitting the envelope of decay curve. The experimental results show that the R-square value of the fitted curve reaches up to 99.999% as compared to the measured data and the repeatability of the tested Q factor is 4.03%, much better than that of the frequency sweeping method. Comparing the measurement data of decay constant method and frequency sweeping method, the former shows better measurement accuracy and higher efficiency. The method is also suitable for the measurements of microsensors with high Q factors.