The detection and study of the rotational motion of space debris, which is affected by environmental factors, is a popular topic. However, relevant research in extremely low-orbit regions cannot be conducted due to a lack of observational data. Here, we fill in the gaps to present the rotational evolution of Tiangong-1 in the 5months prior to reentry. Derived from the changes in the relative distance of its two corner cube reflectors from satellite laser ranging data, the angular momentum of Tiangong-1, which is relatively stable during observation, deviates from its maximum principal axis of inertia and precesses around the normal direction of the orbital plane due to gravity gradient torque at an angle of 23.1 degrees +/- 2.5 degrees. Requiring consistency with the relationship between the angular momentum and precession rate leads to a solution for the rotation rate, which is thus found to increase. This result cannot be explained by any previously developed torque models. Hence, an atmospheric density gradient torque (ADGT) model that considers the torque generated by the change in atmospheric density with orbital altitude at the satellite scale is proposed to explain the rotational acceleration mechanism of extremely low-orbit objects. The numerical results show that the ADGT model provides a non-negligible ability to explain, but cannot fully describe, the acceleration effect. The data on the rotational evolution of Tiangong-1 can provide an important basis for aerodynamic model improvement by addressing minor factors omitted in previous models.