We experimentally studied the transverse mode instability (TMI) threshold of a linearly polarized single-frequency fiber laser amplifier constructed with tapered ytterbium-doped fiber (TYDF) under different bending diameters. The TMI threshold increased from 333 W to 451 W by reducing the bending diameter from 16 cm to 12 cm, which was accompanied by the deterioration of the beam quality from 1.47 to 1.67. The anomalous characteristics between the TMI threshold, bending diameter, and beam quality are mainly attributed to the decreased bending loss of higher-order mode (HOM) content as a result of the increased system heat loads caused by a tight bending-induced loss of amplification efficiency. It is believed that the presented results will provide useful guidelines for the design of high-power single-frequency fiber amplifiers.