This paper presents a cross-dispersion prism-grating device using a plane transmission grating attached directly to a prism, which is different from traditional cross-dispersion grating-prism systems that are based on the reflection grating. Unlike conventional direct-vision grism or constant-dispersion grism in which both the prism and grating have the same dispersion direction, for this device the dispersion directions of the prism and grating are different. The analytical expressions for the cross-dispersion of this device are derived in detail and the formulas of the footprint of the dispersed spectra are given. The numerical results and ray-tracing simulations by ZEMAX are shown. The device provides a compact, small-sized and broadband cross-dispersion device used for the medium resolution spectrometer.