A miniature, broadband, astigmatism-corrected Czerny-Turner spectrometer is proposed. Theories of the broadband astigmatism correction using freeform cylindrical lens are thoroughly analyzed. Comparisons of the freeform cylindrical lens method with those of titling cylindrical lens or wedge cylindrical lens methods are also described. Results show the better spectrometer performance with the new optical design over a broadband spectral range from 300 to 800 nm.