The properties of a nonfocusing collimating parabolic telescope are studied in detail by a ray-tracing method. The best optical quality with respect to coma and astigmatism is calculated for rays close to the optical axis of the telescope. For rectangular fields of view the borders are not sharp because of the aberration. A combination of a parabolic telescope and an echelle-type spectrometer gives very high spectral resolution. Wadsworth, Ebert-Fastie, and other types of spectrometers are equally well suited to be combined with this telescope. For some cases spot diagrams demonstrate the optical performance. In addition, diffraction by the aperture and its implications are discussed.