In order to realize the real-time, secure, and high-speed post-processing for quantum random number generation, this work experimentally takes four independent high-frequency sideband modes from quantum vacuum noise as entropy sources using balanced homodyne measurement. In addition, the paper performs four-channel parallel extraction under a sampling rate of 240 MSa/s and 16-bit analog-to-digital conversion in each channel and achieves multiplex real-time, and high-speed Toeplitz-Hash post-processing in a field programmable gate array (FPGA). The large-scale Toeplitz matrix is decomposed, and multi-cycle distributed processing is performed to ensure the stable operation of hardware. Furthermore, the paper investigates the hardware resource occupancy rate of secure post-processing with different matrix sizes and channel numbers, and finally realizes four-channel Toeplitz-Hash post-processing with an FPGA logical resource occupancy rate of 62% and quantum random number generation with a real-time rate of 10.44 Gbit/s. The cross correlation and mutual information of quantum random numbers between every two channels are below 10^-3 and 10^-6, respectively, and the accumulatively generated quantum random numbers pass the NIST, Diehard, and TestU01 tests. Therefore, this work provides important support for the practical applications of quantum random numbers in high-speed and secure communication.