Superconducting Transition-edge Sensor (TES) is a thermal detector that measures the deposited energy by changing the superconducting film's resistance. Superconducting TES-based single-photon detectors with high detection efficiency, low dark count rate, photon-number and arriving-time resolving capability, are ideal detectors for faint and rapidly varying sources, playing a unique role in studying pulsars, neutron stars, white dwarfs and exoplanets. The critical temperature (T_C) is the key parameter that determines the energy resolution (?E_FWHM) of superconducting TES single-photon detectors, which can be finely tuned by baking the superconducting film or fabricated devices in the air. We studied the characteristics of titanium and titanium/gold bilayer films and the dependence of T_C on baking time (t_baking) and baking temperature (T_baking). It was found that the T_C is logarithmically decreased with t_baking for a fixed T_baking, while it is exponentially decreased with T_baking for a fixed t_baking. By treating the phase-slip parameters as variables, we extended the two-fluid model to extract the key parameters of superconducting TESs including temperature and current sensitivity coefficients from the measured current-voltage curves at different bath temperatures. By adding an M factor to take the excess noise into account, the simulated ?E_FWHM is consistent with the measured one. We then calculated the T_C dependence of ?E_FWHM for a 20 μm×20 μm Ti TES device and found that superconducting TESs with a T_C of less than 170 mK can easily discriminate the photon numbers with a good ?E_FWHM. Finally, we designed and fabricated titanium-based superconducting TES single-photon detectors, which were embedded in an optical cavity to improve the absorption efficiency. The optical cavity is composed of a dielectric mirror with 8 periods of Ta₂O₅/SiO₂ layers and an anti-reflection coating with 2 periods of Ta₂O₅/SiO₂ layers. The refractive index of Ta₂O₅, SiO₂ and titanium film were measured with an ellipsometer, thus the calculated absorption efficiency of the optical cavity at 1 550 nm is nearly 100%, which is in agreement with the measured value with an IR spectrometer. The fabricated superconducting TES single-photon detector with an active area of 20 μm×20 μm is aligned to a single-mode fiber with the help of an IR microscope and a two-dimensional moving stage, which reached a coupling efficiency of nearly 100%. A 1 550 nm pulsed light source is used to measure the optical response. To measure the system detection efficiency (η_sys), we used a calibrated power meter and two precision attenuators to determine the average photon numbered incident (μ_in) on the superconducting TES. The detected photon number (μ_out) was obtained from the height histogram with a large count of pulse responses. Then η_sys is the ratio of μ_out to μ_in, η_sys=μ_out/μ_in. We realized high-performance superconducting TES single-photon detectors with a η_sys of higher than 90% and an ?E_FWHM of 0.5 eV at 1 550 nm. In addition, we developed a superconducting TES single-photon detector to detect 850 nm photons. The thickness of titanium film was chosen to be 53 nm and its T_C is beyond 400 mK, which makes possible to cool it with just a He-3 sorption cooler instead of a dilution refrigerator. While working at 300 mK, the superconducting TES single-photon detector with a η_sys of 13% and an ?E_FWHM of 0.75 eV can still resolve 850 nm photon numbers. Such superconducting TES single photon detectors with high η_sys, good ?E_FWHM and short recovery time pave the way for the detection of rapidly varying sources.