To analyze the stability of traffic flow mixed with manned vehicles as well as connected and autonomous vehicles (CAV), a theory analysis method was proposed. The car-following models were linearized by using Taylor formula. The transfer function theory was used to derive the stability criterion of mixed traffic flow with different CAV proportions. Meanwhile, parametric sensitivity analysis was conducted on acceleration feedback coefficient of CAV. Considering the propagation characteristics of small disturbances under open boundary conditions, numerical simulation experiments on the stability of mixed traffic flow were designed. Research results show that the unstable speed range of CAV was within the unstable speed range of manned vehicles. The increase of CAV proportion was helpful to transform the traffic flow from unstable state to stable state. The larger the acceleration feedback coefficient of CAV was, the larger the stability regions of the mixed traffic flow with respect to CAV proportion and equilibrium speed would be. When the CAV proportion increased to 23%, the mixed traffic flow was stable within full equilibrium speeds. The research findings can theoretically calculate stability regions of CAV mixed traffic flow, and can provide evidence for analyzing stability of mixed traffic flow from the perspectives of CAV proportions and equilibrium speeds.