Dielectric polymer film capacitors with a high-power density as well as efficient charge and discharge rates have great potential for application to fulfill the miniaturized and lightweight requirements of the electronic and stationary power systems. It was reported that the elastic recovery rate and energy storage density of poly (vinylidene fluoride-chlorotrifluoroethylene) [P(VDF-CTFE)] polymer film can be enhanced through thermostatic uniaxial stretching. But it is unknown about the relationship between the stretching rate and above properties. In this study, we investigated the effect of different stretching rates on the conformation, elastic recovery, dielectric constant, and energy storage density of stretched P(VDF-CTFE) polymer films. It was found that the stretching rate significantly affected the formation of polar$\beta$-crystal phase, causing different dielectric properties. The degrees of elastic recovery of P(VDF-CTFE) film vary with stretching rates. Among them, the elastic recovery rate of the P(VDF-CTFE) 94/6 film is 46.5% at a stretching rate of 15 mm/min, the dielectric constant is 12.25 at 100 Hz, and the energy density reaches 3.95 J/cm³ with the energy loss of 39% at 200 MV/m field.Dielectric polymer film capacitors with a high-power density as well as efficient charge and discharge rates have great potential for application to fulfill the miniaturized and lightweight requirements of the electronic and stationary power systems. It was reported that the elastic recovery rate and energy storage density of poly (vinylidene fluoride-chlorotrifluoroethylene) [P(VDF-CTFE)] polymer film can be enhanced through thermostatic uniaxial stretching. But it is unknown about the relationship between the stretching rate and above properties. In this study, we investigated the effect of different stretching rates on the conformation, elastic recovery, dielectric constant, and energy storage density of stretched P(VDF-CTFE) polymer films. It was found that the stretching rate significantly affected the formation of polar$\beta$-crystal phase, causing different dielectric properties. The degrees of elastic recovery of P(VDF-CTFE) film vary with stretching rates. Among them, the elastic recovery rate of the P(VDF-CTFE) 94/6 film is 46.5% at a stretching rate of 15 mm/min, the dielectric constant is 12.25 at 100 Hz, and the energy density reaches 3.95 J/cm³ with the energy loss of 39% at 200 MV/m field.