Hyperspectral remote sensing technology is an optical remote sensing technology developed on the basis of imaging spectroscopy, which can realize comprehensive observation of spatial information, spectral information and radiation information. The imaging spectrometer adopting the Prism-Grating-Prism (PGP) spectroscopic element avoids the off-axis problem of traditional prism-type and grating-type imaging spectrometers, and is conducive to the miniaturization and compactness of imaging spectrometers. Aiming at the problem that the spectral smile of coaxial PGP imaging spectrometer is difficult to correct, this paper proposes a method to rectify the curvature of spectral line by using curved slit and distortion of the collimator lens and focusing lens. On the basis of retaining the advantages of PGP such as high diffraction efficiency and coaxial optical path, this method can correct spectral smile and keystone of the instrument. In this paper, the prism-grating-prism vector dispersion model is established by focusing on the influence of lens distortion, the number of grating lines and prism angle on spectral smile and keystone. By tracing the light vector and analyzing the intersection between the light vector and the image plane after the light vector passes through the PGP element with different parameters, the influence of different parameters on the smile was analyzed. It is worth noting that when the shape of the slit changes, the direction of the initial light vector also changes. Therefore, this model can also analyze the effect of the slit shape on the spectral smile and keystone. Further, the prism-grating-prism vector dispersion model is used to analyze the spectral line bending characteristics of coaxial PGP spectroscopic elements: when the coaxial condition is met, the PGP imaging spectrometer will inevitably have a large smile, and the spectrum is bent in the short-wave direction. After adjusting the prism Angle, the number of grating lines and the lens distortion, we analyzed the smile size of the combination of the above parameters, and came to an optimistic conclusion: the smile problem of the imaging spectrometer could not be eliminated only by changing the prism, grating and lens. However, the smile can be corrected well by the method of bending the slit and matching the appropriate lens distortion. In order to improve the versatility of this method, this paper gives an objective function for correcting spectral curvature and spectral line curvature by using the PGP vector dispersion model, and uses genetic algorithm to optimize the objective function and calculate the best combination of slit shape and lens parameters quickly. In order to verify the feasibility of this method, this paper uses the calculation results of this method to design a curved slit PGP imaging spectrometer with a slit length of 22 mm, an operating wavelength of 400~800 nm, a spectral resolution of 3 nm, and an F number of 3.5 which has a spectral curvature of less than 2 μm and a spectral line curvature of less than 2 μm. The optical system has a diffuse spot radius of less than 5.4 μm in the wavelength range of 400~800 nm, and can distinguish slit images with a spectral interval of 2 nm. The energy concentration of all fields of view can reach 90% in the 2×2 pixel scale. The design results show that the use of curved slit and distortion of the collimator lens and focusing lens can effectively correct the curve of the spectral line, which has important guiding significance for the design of the coaxial PGP imaging spectrometers. In this article, we calculated the optimal slit shape and lens parameters for different slit lengths and different grating parameters, which proved that the method had universal applicability.