To address the problem of real-time processing of ultra-wide bandwidth pulsar baseband data, we designed and implemented a pulsar baseband data processing algorithm (PSRDP) based on GPU parallel computing technology. PSRDP can perform operations such as baseband data unpacking, channel separation, coherent dedispersion, Stokes detection, phase and folding period prediction, and folding integration in GPU clusters. We tested the algorithm using the J0437-4715 pulsar baseband data generated by the CASPSR and Medusa backends of the Parkes, and the J0332+5434 pulsar baseband data generated by the self-developed backend of the NanShan Radio Telescope. We obtained the pulse profiles of each baseband data. Through experimental analysis, we have found that the pulse profiles generated by the PSRDP algorithm in this paper are essentially consistent with the processing results of Digital Signal Processing Software for Pulsar Astronomy (DSPSR), which verified the effectiveness of the PSRDP algorithm. Furthermore, using the same baseband data, we compared the processing speed of PSRDP with DSPSR, and the results showed that PSRDP was not slower than DSPSR in terms of speed. The theoretical and technical experience gained from the PSRDP algorithm research in this article lays a technical foundation for the real-time processing of QTT (Qi Tai radio Telescope) ultra-wide bandwidth pulsar baseband data.