The time-resolved soft x-ray spectrometer (TSXS) aboard on the X-ray Pulsar Navigation Test Satellite is an x-ray timing spectrometer covering the energy range of 0.5 to 10 keV. It is China’s first focusing x-ray telescope launched into space orbit. The optical system of TSXS is an x-ray grazing incidence focusing system with a field of view 15 arc min, which is nested with 4 parabolic mirrors with a focal length of 1150 mm. The focal plane detector of TSXS uses a silicon drift detector. From April to June 2016, ground calibration was carried out on TSXS, including the optical axis determination, calibration of energy linearity and energy resolution, calibration of time resolution and photon arrival time accuracy, and calibration of mirrors’ reflectivity. After the launch on November 10, 2016, the in-orbit calibration and performance verification of the telescope was carried out, including the optical axis determination, the performance of energy response, the performance of time accuracy, the calibration of effective area, and the evaluation of telescope sensitivity. After calibration and verification on the ground and in orbit, the photon energy measurement error of the telescope is better than 0.5% at energies above 1.5 keV, the energy resolution is better than 156 eV at 6.4 keV, the time resolution is <1  μs, the photon arrival time measurement accuracy is <302  ns, and the telescope in-orbit background is <4.16  ±  1.42  ×  10^−  3  photons  /  s (0.5 to 3 keV, 40°N to 40°S, not including South Atlantic Anomaly). The telescope has an in-orbit observation sensitivity of 2.09  ×  10^−  3  photons  /  cm²  /  s  /  keV (0.5 to 3 keV, T  =  1000  s, and n_σ  =  5).