We present a novel, to the best of our knowledge, InGaAs/InAlAs single-photon avalanche diode (SPAD) with a triple-mesa structure. Compared with the traditional mesa structures, the horizontal distribution of the electric field decreases dramatically, while the peaks of the electric field at the mesa edges are well eliminated in the triple-mesa structure, leading to an excellent suppression of the surface leakage current and premature breakdown. Furthermore, the temperature coefficient of the breakdown voltage was measured to be as small as 37.4 mV/K within a range from 150 to 270 K. Eventually, one of the highest single-photon detection efficiencies of 35% among all the InGaAs/InAlAs SPADs with a decent dark count rate of ${3.3} \times {{10}^7}\;{\rm Hz}$ was achieved at 240 K. Combined with the inherent ease of integration of the mesa structure, this high-performance triple-mesa InGaAs/InAlAs SPAD provides an effective solution for the fabrication of SPAD arrays and the on-chip integration of quantum systems.