Abstract In the two-dimensional positioning method of pulsars, the grid method is used to provide non-sensitive direction and positional estimates. However, the grid method has a high computational load and low accuracy due to the interval of the grid. To improve estimation accuracy and reduce the computational load, we propose a fast two-dimensional positioning method for the crab pulsar based on multiple optimization algorithms (FTPCO). The FTPCO uses the Levenberg-Marquardt algorithm, three-point orientation method, particle swarm optimization and Newton-Raphson-based optimizer to substitute the grid method. Firstly, to avoid the influence of the non-sensitive direction on positioning, we take orbital error and the distortion of the pulsar profile as optimization objectives and combine the grid method with the Levenberg-Marquardt algorithm or particle swarm optimization to search for the non-sensitive direction. Then, on the sensitive plane perpendicular to the non-sensitive direction, the three-point orientation method is proposed to fast search the sensitive direction and sub-sensitive direction. Finally, the Newton-Raphson-based optimizer is employed on the sensitive and sub-sensitive directions to achieve two-dimensional positioning of the Crab pulsar. The simulation results show that the computational load of the FTPCO is reduced by 89.4% and the positioning accuracy of the FTPCO is improved by approximately 38% compared with the grid method. The proposed method has the advantage of high real-time accuracy and does not fall into the local optimum.