With the application of lightweight composite materials in reentry vehicle, elastic vibration problem often appears in autopilot designing. Considering flexible body dynamics and actuator dynamics, stability of flight path angle tracking autopilot is analyzed utilizing frequency stability theory. Influence of rate inner loop and hinge moment on the gain and phase margin is obtained. Furthermore, lag correction of autopilot is proposed according to the analysis results of amplitude frequency and phase frequency characteristic curves. After lag correction, the elastic vibration amplitude is attenuated, while the phase margin is still acceptable. The analysis results and correction method can provide reference for autopilot design of reentry vehicle with elastic vibration problem.