In this work, electronic and transport properties of a pristine sawtooth penta-graphene nanoribbon (SSPGNR) and sawtooth penta-graphene nanoribbons doping with Silicon, Nitrogen, Phosphorus (Si-SSPGNR, N-SSPGNR, P-SSPGNR) are studied systematically by density-functional theory (DFT) in combination with the nonequilibrium Green's function formalism. Pristine sample and three doped samples in a similar position are terminated with H atoms. To explore in detail the electronic and transport features, we compute and discuss about the structure properties, band structure, density of states, I-V curve, and transmission spectrum. Our result shows that doping affects dramatically affects on the electronic nature and the I-V characteristic of samples. More specifically, the current intensity of N-SSPGNR and P-SSPGNR increase by 9 orders of magnitude compared to that of SSPGNR while the one of Si-SSPGNR has negligible change. However, there are also considerable differences in I-V curves of samples doping with N and P. Our findings indicate that doping by N and P can effectively modulate the electronic and the transport properties of SSPGNRs, which has not been studied so far.