This paper dealt with the measurement and analysis of partial discharge (PD) under high voltage direct current (HVDC) in SF6 gas. Electrode systems such as a protrusion on conductor (POC), a protrusion on enclosure (POE), a crack on epoxy plate and a free particle (FP) were fabricated to simulate the insulation defects. The analysis system was designed with a Time-Frequency (T-F) map algorithm programed based on LabVIEW. This can arrange the acquired PD pulses into frequency and time domain. A HVDC power source is composed of a transformer (220 V/50 kV), a diode (100 kV) and a capacitor (50 kV, 0.5 ${mu}F$). The gap between the electrodes is 3 mm, and the $SF_6$ gas was set at 5 bar. PD pulses were detected by a 50 ${Omega}$ non-inductive resistor. In the analysis, PD pulses were distributed below 0.5 MHz and 20 ns ~ 35 ns for the POC, 0.7 MHz ~ 1.7 MHz, below 0.6 MHz and 10 ns ~ 40 ns and 60 ns ~125 ns for the POE, below 0.1 MHz and 135 ns ~ 215 ns for the crack, and below 1.6 MHz and 250 ns for the FP.