In ultra-high-speed large-capacity optical fiber communications and high-power ultra-fast fiber laser systems, chirped fiber gratings are widely used to compensate and manage dispersion. The dispersion coefficient matching degree directly determines the output quality and application range of the optical pulse signal. Compared with other dispersion compensation technologies, the fiber grating preparation process is simple, has good repeatability, and can be flexibly designed according to actual needs, which has great advantages. However, previous fiber grating dispersion analysis usually only considers the influence of second-order linear dispersion and ignores issues such as pulse distortion caused by high-order nonlinear dispersion mismatch, resulting in unsatisfactory actual use results. Different from the traditional coupling mode theory and transmission matrix analysis method, this paper establishes a new set of dispersion analysis mathematical models for nonlinear chirped fiber grating based on the group dispersion delay principle of optical fiber. The numerical relationship between the Bragg reflection wavelength, the dispersion parameter and the dispersion slope is deduced, which greatly reduces the complexity of the previous calculation process and has strong practicality. In practical application scenarios, as long as the specific dispersion parameters that need to be compensated in the fiber laser system are understood, this numerical relationship can be used to calculate the corresponding chirped fiber grating period distribution, thereby achieving the best system output. Based on this mathematical model and the current common femtosecond fiber laser product specifications on the market, we used UV scanning exposure technology combined with the phase mask method to design and prepare two nonlinear chirped fibers for high-power femtosecond fiber laser pulse broadening. The grating can respectively stecher the incident seed pulse in the 1 030 nm band to more than 150 ps or 1 ns, while meeting the third-order dispersion matching requirements in the optical system. In addition, based on the classic Michelson interference principle, we built a set of spectral interference dispersion measurement devices and conducted actual dispersion tests on the two nonlinear chirped fiber gratings we produced. Compared with other measurement methods, this device has simple principle, low cost, high measurement accuracy, wide range and strong practicability. It is very suitable for dispersion measurement of special optical fibers such as fiber gratings and photonic crystal fibers. Experimental results show that the reflection bandwidths of the two nonlinear chirped fiber gratings have reached 17 nm and 11 nm respectively, the dispersion parameters are -10.3 ps/nm and -107 ps/nm respectively, the dispersion slopes are -0.013 ps/nm² and -0.087 ps/nm² respectively, and the reflectivity reaches more than 60%, which basically meets the requirements of practical applications. Taking into account the processing accuracy of fiber gratings and phase masks, as well as the systematic errors introduced by the dispersion measurement device and the approximation of theoretical calculations, the experimental results are basically consistent with the design parameters, proving the correctness and feasibility of this mathematical model. The research results can provide new solutions and references for the design, analysis and production testing of nonlinear chirped fiber gratings. It is foreseeable that the model established can be extended to chirped volume gratings and other composite gratings with the same structure.