Based on the mode coupling theory of fiber grating, the transmission spectrum characteristics of cascaded long- and short-period fiber grating were analyzed by transmission matrix method. The transmission matrices of long-period fiber grating (LPFG), connected fiber and short-period fiber Bragg grating (FBG) were obtained by the coupling mode equation, and then the total transmission matrix of cascaded fiber gratings could be obtained by multiplying them. Finally, the transmission spectrum of long- and short-period cascaded fiber Bragg grating (CLBG) was obtained by combining boundary conditions. The transmission spectrum of CLBG was further simulated numerically and verified by experiment. The experimental results show that there are two resonant peaks formed by the coupling of core mode and cladding modes in the transmission spectrum of CLBG, which are consistent with the simulation results. It verifies the feasibility of the transmission matrix method to solve the transmission spectrum of CLBG, and provides theoretical support for the wide application of CLBG in the field of multi-parameter sensing and measurement.