To reduce the computational cost, a Fast position and velocity joint determination(FPVD) method based on the Near-maximum likelihood(NML) and the Least square method(LSM) is proposed for X-ray pulsar navigation. Considering the fact that the Doppler effects caused by the velocity of the spacecraft alters the X-ray pulse Time-of-arrival(TOA), we adopt the NML to obtain multi-TOAs, and then utilize the LSM to estimate the variation of TOAs instead of the pulsar profile distortion adopted by the Maximum-likelihood(ML) estimation method. Finally, according to the variation value and TOAs, the position and velocity information of the spacecraft are calculated. The simulation results have demonstrated that the FPVD method is far faster than the ML estimation method, and its accuracy approaches the CramerRao lower bound(CRLB). To reduce the computational cost, a Fast position and velocity joint determination (FPVD) method based on the Near-maximum likelihood (NML) and the Least square method (LSM) is proposed for X-ray pulsar navigation. Considering the fact that the Doppler effects caused by the velocity of the spacecraft alters the X-ray pulse Time-of-arrival (TOA), we adopt the NML to obtain multi-TOAs, and then utilize the LSM to estimate the variation of TOAs instead of the pulsar profile distortion adopted by the Maximum-likelihood (ML) estimation method. Finally, according to the variation value and TOAs, the position and velocity information of the spacecraft are calculated. The simulation results have demonstrated that the FPVD method is far faster than the ML estimation method , and its accuracy approaches the CramerRao lower bound (CRLB).