Conventional Czerny-Turner spectrometers exhibit keystone distortion due to astigmatism, which affects their performance when a linear array photomultiplier tube (LaPMT) is used as the detector. We propose a novel optical design of a crossed Czerny-Turner spectrometer with a 32-channel LaPMT detector. We use convergent illumination of the grating to modify the astigmatism of the off-axis spherical mirrors, and the image spot radius at the central wavelength in the sagittal plane is matched with the width of the LaPMT. A first-order equation is derived for the elimination of the broadband keystone distortion. After optimization, the image size over the entire bandwidth matches well with the LaPMT size, which is consistent with the theory, and the spectral resolution is ∼4 nm per channel.