To overcome the difficulties of complex structure and serious nonlinear dispersion in prismatic imaging spectrometer the coaxial linear dispersion prismatic imaging spectrometer is investigated in this paper. A mathematical model of symmetric triple prisms’ beam splitting system is constructed with prism's dispersion equation, and the prisms assemble of direct view is obtained. Then the factors affecting dispersion linearity are analyzed. The refractive index and dispersion rate of prism material impact dispersion linearity most while the influence of incident angle is very small. The way to improve dispersion linearity is given and the refractive index condition meeting the requirement of dispersion linearity of prisms is obtained. It provides important basis to select the initial structure for coaxial linear dispersion triplet prisms of imaging spectrometer. On condition that the working band of 400~1 000 nm, center wavelength deviation angle 0°, the maximum dispersion angle 0.6°, object numerical aperture 0.15 and spectral resolution 5 nm, we succeed in designing coaxial linear dispersion triplet prisms. Digital simulation with ZEMAX is performed, and the results are in accordance with theoretical analysis.