A pure rotational Raman lidar has become one of valid methods of profiling atmospheric temperature. However, its proper operation generally needs a certain collocated device of atmospheric temperature to calibrate three retrieval coefficients. This fact seriously restricts the applications of pure rotational Raman lidar in the meteorology and environment fields. In order to execute the detection technique of atmospheric temperature without calibration, we present and design a pure rotational Raman lidar based on the dependence of atmosphere molecular rotational Raman spectral envelope on temperature. It is configured with a laser having a pulse energy of 300 mJ, a pulse repetition rate of 20 Hz, and a Cassegrain telescope with a clear aperture of 250 mm. A two-stage multi-channel pure rotational Raman spectroscopic filter is proposed to extract efficiently the rotational Raman spectral lines with more than 70 dB suppression to the elastic-scattering optical signals. It is configured with one blazed diffraction grating, one convex lens, one linear fiber array and seven groups of fiber Bragg gratings. The blazed diffraction grating and fiber Bragg grating are separately utilized as the primary and secondary spectroscope. The tailor-made fiber array, which is composd of ten single mode fibers of 460-HP type and one multi-mode fiber, is designed to transfer the spectral signals. One end face of multi-mode fiber lies in the focal point of telescope, and then it transfers the lidar echo signals to the pure rotational Raman spectroscopic filter. The other end face of multi-mode fiber lies in the focal point of convex lens. The ten single mode fibers are used to transfer the optical signals from the primary spectroscope to the secondary, and their end faces lie in the focal plane of convex lens. Six pure rotational Raman spectral lines of nitrogen molecule in the anti-Strokes branch are chosen under the condition of the 0.09-nm forbidden band, with the consideration of the relationship between the pure rotational Raman spectral lines of nitrogen and oxygen molecules. While the excited laser wavelength is 532 nm, their central wavelengths are 530.76 nm, 529.86 nm, 529.41 nm, 528.51 nm, 527.62 nm, and 527.17 nm, respectively. Their corresponding positions of fiber end faces on fiber array are 156 m, 407 m, 532 m, 782 m, 1031 m, and 1156 m. Compared with these pure rotational Raman spectral lines, the elastic scattering signal lies on the other side of the focal point of convex lens, which improves the spectral purity of pure rotational Raman spectral lines. A retrieval algorithm of absolute detection technique is presented based on the least square principle. The performance of this lidar is simulated based on the U. S. standard atmospheric model. Simulation results show that this designed lidar can achieve the extraction of the pure rotational Raman spectral lines of nitrogen molecules, and that the atmospheric temperature profile obtained from absolute retrieval algorithm within a measurement time of 17 min can be up to 2.0 km with less than 0.5-K deviation. This pure rotational Raman lidar without calibration will provide a new detection method and retrieval scheme for atmospheric temperature profile.