The rapidity limitation problem of three-loop acceleration autopilot widely used in tactical missiles is studied. Based on the math-ematic model of autopilot, the relation between close-loop poles and system bandwidth was firstly constructed, and the concyclic rule of pole-placement was proved necessary to obtain ideal system response. Then according to the design of system bandwidth and the placement of close-loop system pole-zeros, the constraints on the autopilot rapidity limitation was analyzed, which including the bandwidth of high fre-quency components, the limitation of the fin rate, and the close-loop zeros. Therefore the mathematic description of autopilot rapidity limi-tation is concluded, which is validated by autopilot design examples.