Physical random number, which is non-reproducible and non-periodical, has attracted much attention due to its potential applications in various fields such as secure communication, statistical analysis, and numerical simulation. Recently, fast physical random number generators based on optical chaotic entropy sources have been demonstrated to reach a rate of up to several hundreds of Gbit/s. Although many efforts have been made to optimize the schemeis of chaotic-based random number generation, most of them are based on distributed feedback semiconductor lasers and can only generate single-channel physical random number. After taking into account the costs and technological applications, the multi-channel physical random number generation technique needs developing. On the other hand, vertical-cavity surface-emitting lasers (VCSELs) can simultaneously emit two orthogonally polarized components under appropriate parameter conditions, and then each polarized component can be used as an entropy source for generating random number. As a result, VCSEL-based chaotic entropy sources may be suitable for multi-channel random number generation. In this work, a scheme for achieving multi-channel physical random number is proposed. Also the influence of the coupling parameters on the performance of the randomness of final bit sequences is investigated. For such a scheme, two orthogonally mutually coupled VCSELs are used to supply four-channel chaotic signals with a comparable output power and weak time-delay signature (TDS). The four-channel chaotic signals, which serve as chaotic entropy, are quantized by 8-bit analog-to-digital converters (ADCs) with 20 GHz sampling rate, and then the m least significant bit (m-LSB) post-processing method is adopted for generating final four-channel random bit sequences. Firstly, based on the spin-flip mode of VCSELs, the influences of coupling strength and frequency detuning on the dynamics of two orthogonally mutually coupled 1550 nm VCSELs are analyzed. Next, the optimized parameter regions for generating four-channel chaotic signals with comparable output power and weak TDS are preliminarily determined. For a given optimized value of coupling strength and different frequency detunings within the optimized parameter regions, the generated four-channel chaotic signals are taken as the entropy sources for obtaining final bit sequence by quantizing the 8-bit ADC and m-LSB post-processing. Finally, the randomness of the four final bit sequences is tested by NIST SP 800-22 statistical test suite, and the regions of preferred coupling parameters for simultaneously generating four-channel random numbers are determined.