The Rossi X-ray Timing Explorer (RXTE) has made hundreds of observations on three famous young pulsars (PSRs) B0531+21 (Crab), B1509-58, and B0540-69. Using the archive RXTE data, we have studied the phase-resolved spectral properties of these pulsars in details. The variation of the X-ray spectrum with phase of PSR B0531+21 is confirmed here much more precisely and more details are revealed than the previous studies: the spectrum softens from the beginning of the first pulse, turns to harden right at the pulse peak and becomes the hardest at the bottom of the bridge, softens gradually until the second peak, and then softens rapidly. Different from the previous studies, we found that the spectrum of PSR B1509-58 is significantly harder in the center of the pulse, which is also in contrast to that of PSR B0531+21. The variation of the X-ray spectrum of PSR B0540-69 seems similar to that of PSR B1509-58, but with a lower significance. Using the about 10 years of data span, we also studied the real time evolution of the spectra of these pulsars, and no significant evolution has been detected. We have discussed about the constraints of these results on theoretical models of pulsar X-ray emission.RXTE has made hundreds of observations on the three young pulsars that we studied, which were listed in Table. 3. The total exposure time of PSRs B0531+21, B1509-58, and B0540-69 is 172, 578, and 2,663 ks, respectively ( Table. 3), and with such plenty of data we can perform detailed phase-resolved spectroscopic study. The Event mode data were selected for our analyses, so as to have good time resolution and enough spectral channels.Heasoft (v6.10) was used to process the observational data as follows: (1) Create the filter file for each observation with XTEFILT; (2) generate the Good Time Interval (GTI) file by MAKETIME using the filter file; (3) using the GTI file to create the "good" events file with GROSSTIMEFILT; and (4) remove the clock events from the event mode data by SEFITER and FSELECT. The resulted new events data will be used in the timing and