The effect of Pulse Density Force Feedback (PDFF) on the performance of a micro-machined gyroscope was investigated and a closed-loop circuit for the micro-machined gyroscope was designed based on a mechanical and electrical ∑Δ modulator. Firstly, from the equivalent forms of a sense mode for the micro-machined gyroscope, the effect principle of PDFF on the performance of sense mode was analyzed and it was divided into two parts: negative stiffness and gain effects. The analysis shows that the negative stiffness is independent on the input of angular rate. Then, the relationship between pulse density and input angular rate, and that between input range and high level feedback pulse were built based on the theory of closed-loop detection. Finally, the circuit parameters were calculated by using the range design index and the actual parameters of gyroscope, then these parameters were simulated in Simulink. Simulation result shows that the parameters satisfy the design objective, and the nonlinearities between average pulse density and angular rate are 3.6×10-6, 3.07% and 5.12%, respectively, when the quadrature error equivalent input angular rates are 0(°)/s, 30(°)/s and 50(°)/s. Two gyro sample I and II with the quadrature error equivalent input angular rates of 30.4(°) /s and 47.3(°)/s were tested, and the experiment results show that the effect of PDFF on the negative stiffness doesn′t change with the pulse density; and the nonlinearities between the average pulse density and angular velocity are 2.9% and 4.8%, respectively. The experimental and simulation results get a better match.