In practical applications of high-speed quantum random number generators, using Toeplitz matrices as a post-processing method to extract the randomness of quantum random numbers has become a major technology roadmap. However, Toeplitz matrices are more suitable for hardware calculations than for software calculations and typically require that specialized field programmable gate array (FPGA) circuits be constructed for fast calculations. Based on the quantum random generator of spontaneous emission amplification (ASE), a fast post-processing method based on a simple hash function is proposed. The time complexity of this method is only O(N), which is less than O(NlogN) of a Toeplitz matrix, and compared with another commonly used post-processing method, least significant bit (LSB) post-processing has higher efficiency in random number extraction. The random number calculated by the proposed post-processing method in the experiment passes the randomness test of the national institute of standards and technology (NIST) in the United States.