Atmospheric temperature and humidity profile data are basic inputs for numerical weather prediction and climate change assessments, and they are considered indispensable for other scientific research. Improving weather forecast and climate prediction ability by using high spectral satellite data to accurately and quantitatively invert high precision temperature and humidity profiles is of great significance. This paper uses hyperspectral infrared radiation data from the next generation cross-track infrared detector CrIS (Cross-track Infrared Sounder) on the Suomi-NPP (National Polar-orbiting Partnership) satellite as well as reanalysis data of temperature and humidity profiles from the ECMWF (European Centre for Medium-Range Weather Forecasts). In this paper, the D-R (Dual-Regression) inversion algorithm is used to study the inversion of high temperature and humidity profiles. Then, it is compared with measured temperature and humidity profile data from June to Septemberof each year between 2014 and 2016 at the Shanghai Baoshan site and the official temperature and humidity product inversion by NOAA (National Oceanic and Atmospheric Administration)'s official NUCAPS (NOAA Unique Combined Atmospheric Processing System) algorithm. The results show that the total BIAS of the atmospheric temperature profiles retrieved by the D-R algorithm, based on the background field using ECMWF's temperature and humidity reanalysis data, is basically within 1K, and the RMSE (root mean square error) is basically within 2 K, which is equivalent to the NUCAPS algorithm's inversion accuracy. In the lowest layer of the atmosphere, the inversion accuracy of the D-R algorithm remains within 2 K, which is better than the NUCAPS algorithm (RMSE index). The relative humidity at an inversion height below 300 hPa is of the same accuracy as the NUCAPS algorithm, when the RMSE is less than 20% and the BIAS is less than 10%; hence, the inversion result is good and stable. However, when the height is above 300 hPa, the error of the inversion D-R algorithm increases to 30% and the inversion accuracy is reduced.