Most of the current ultraviolet (UV) optical lenses have narrow working band, which results in the decrease of their application adaptability. It is becasue of the fewer lens materials for UV lens design, and further it is difficult for the correction of UV color aberration. By applying the optical structure of negative-positive lenses overlapping distribution together with quasi-double Gaussian symmetry, as well as utilizing the wide spectral transmittance of fused quartz material and calcium fluoride material, an optical system with wide ultraviolet spectrum was designed, which also had the advantages of large relative aperture, wide field of view and high resolution. Its working wavelength was from 240 nm to 360 nm and the UV working bandwidth reached to 120 nm. All of the lenses in the designed UV optical system were spherical lenses, which could be fabricated and measured easily. Taking the central wavelength of 300 nm as the reference wavelength, the maximum lateral color aberration of the designed UV optical system was less than one pixel size over the full field of view. In the cut-off frequency of 50 lp·mm^-1, the modulation transfer function (MTF) value was better than 0.4. The root mean square (RMS) value of image spot diagram in each field was better than 10 μm. The design results show that the designed UV optical system with wide UV spectrum has good imaging quality, high resolution and small color aberration, which satisfies the design requirements.