This paper presents a novel grating spectrometer design that combines a convexly cylindrical mirror with a concavely cylindrical varied line spacing grating to achieve an extreme resolving power of 33000-70000 in the photon energy range of 0.6-1.5 keV for a Gaussian light source with effective meridional size of 30 μm (root mean square) at an upstream initial object distance of 10 m. This type of spectrometer can be used to diagnose the radiation spectrum of a soft X-ray free electron laser and properly measure the spectral distribution and the detailed structure of the self-amplified spontaneous emission mode due to its extremely high resolving power. The overall optical aberrations of the system are well analyzed and compensated, providing an excellent flat field at the detector domain throughout the entire spectral range. A machine learning support vector machine algorithm is introduced into explore the optimal system to deliver the desired resolving performance. In addition, to enhance the spectral intensity and detection efficiency simultaneously, a sagittal confinement focusing mirror is introduced into the optical path of the spectrometer to reduce the astigmatism in spectral imaging.