A novel hyperspectral imaging spectrometer controlling spatial and spectral resolution individually has been proposed. This imaging spectrometer uses a zoom lens as a fore-optics and a focusing lens. It can change the spatial resolution fixing the spectral resolution or the spectral resolution fixing the spatial resolution. Here, the concept and the principle of the hyperspectral imaging spectrometer with the novel zooming function are presented, and, the collimator lens and the zoom lens as a focusing lens are designed. The collimator lens of the imaging spectrometer is designed through the third-order aberration correction by using an iterative process, which is a new method for an initial design. In the method, the aberration of each group is calculated individually and iteratively, under the constraint that aberrations of one group are compensated by the other groups. By using a lens module and the third-order aberration theory, we have presented the initial design of four-group zoom lens with an external entrance pupil. And the optimized zoom lens with a focal length of 50 to 150 mm is obtained from the initial design by the optical design software. As a result, by combining the designed collimator lens and the focusing lens, the imaging spectrometer shows satisfactory performances in wavelength range of 450 to 900 nm.