We propose a new type Fabry-Perot cavity based on dynamic grating in Er-doped fiber and fiber Bragg grating. The dynamic grating model is established through two-level system of Er-doped fiber. We calculate the reflection and transmission of the dynamic grating and the Fabry-Perot cavity based on semi-classical interactional theory and transfer matrix method, and analyze the influence of some parameters on reflection spectra of the dynamic grating and Fabry-Perot cavity. An important feature of the proposed Fabry-Perot cavity is that its output spectra can be dynamically tunable by parameters modulation, in which the parameters include Rabi frequency of the coherent probe field in the dynamic grating, the length of the Er-doped fiber, the refractive index modulation depth of the fiber Bragg grating, the cavity length of the Fabry-Perot cavity and so on. Compared with the Fabry-Perot cavity based on two fiber Bragg gratings with fixed parameters, the proposed Fabry-Perot cavity is more flexible, and is more beneficial for mode selection. It can overcome the asymmetrical drawback of the two fiber Bragg gratings in Fabry-Perot cavity (such as different Bragg wavelengths, refractive index modulation depths of Bragg grating). The proposed Fabry-Perot cavity has potential applications in fiber-optic communication and fiber sensors.