The mechanical properties of paper are mainly characterized by tensile strength. According to GB/T 12914—2008, this indicator is usually tested with a tensile machine. However, this method requires a large sample size and many samples, which is unsuitable for precious paper cultural relics. In this work, Thermomechanical Analyzer (TMA) is used for mechanical testing of paper cultural relics for the first time to establish a new evaluation method by taking advantage of its precise and nondestructive feature. The environmental changes in the Qianlong Garden of the Palace Museum were monitored, and the aging conditions were designed based on the monitoring results. UV, dry-heat, and humid-heat accelerated aging experiments were carried out on the handmade bamboo paper, which is usually used to restore Pengbihushi in the Palace Museum. TMA, SEM and FTIR were used to test the changes in tensile strength, micro-morphology, and chemical structure of bamboo paper samples before and after aging to analyze the aging characteristics of bamboo paper. The results show that TMA can effectively measure the mechanical strength of bamboo paper with low strength after aging. The tensile strength of bamboo paper after humid-heat aging was the highest (up 1.01%), followed by dry-heat aging (down 15.11%), and after UV aging the lowest (down 63.85%). Correspondingly, it was observed by SEM that there was no obvious change in the fiber structure of the humid-heat and dry-heat aging samples, but the fiber structure of the UV aging samples showed obvious fracture and damage. Infrared spectroscopy analysis also showed that the UV aging sample had the lowest absorption peak in the cellulose fingerprint region, indicating that the cellulose degradation was the most serious. The three test results can confirm each other. In addition, the size of the sample required by TMA is only at the millimeter level (10~20 mm in length, about 1 mm in width), which is much smaller than that of a conventional tensile machine. Moreover, the TMA test only requires about 7 samples to achieve good repeatability and accuracy. TMA has good applicability to low strength paper, so it is expected to explore further the possibility of applying TMA to precious ancient paper with extremely low strength.