Optical chaos based on semiconductor laser (SL) has attracted much attention due to its potential application in various fields such as secure optical communication, chaotic radar, fast physical random bit generation, etc. By introducing external perturbations such as optical feedback, optical injection or optoelectronic feedback, SL can be driven into chaotic dynamic state. In general, an obvious time-delay signature (TDS) can be observed in a chaotic SL system with optical feedback, which is undesirable in some applications. So far, several schemes have been reported on the suppression of the TDS in chaotic SL systems, which are mostly based on external cavity feedback systems or mutually coupled systems. In this work, a novel scheme for suppressing TDS to generate multi-channel high-quality chaotic signals is proposed and numerically simulated based on a ring system composed of three unidirectionally polarization-rotated coupled 1550 nm vertical-cavity surface-emitting lasers (1550 nm-VCSELs). In this scheme, the output from the first 1550 nm-VCSEL passes through an optical circulator (OC), a Faraday rotator (FR) and a variable attenuator (VA), and then is injected into the second 1550 nm-VCSEL. The output from the second (third) 1550 nm-VCSEL passes through a similar path mentioned above, and then is injected into the third (first) 1550 nm-VCSEL. The polarization direction and the strength of injection light are controlled by the FR and VA, respectively. Adopting the spin flip model (SFM), the polarization-resolved dynamical characteristics of the three VCSELs in the ring system are analyzed. By the aid of self-correlation function (SF) and mutual information (MI), the influences of the coupled strength and frequency detuning on the TDS of polarization-resolved chaotic signal output from the three VCSELs are discussed. The results show that through selecting suitable coupling strength and frequency detuning, both the X-polarization component (X-PC) and Y-polarization component (Y-PC) in the three VCSELs can simultaneously be lased with comparative output powers, and the TDSs of these polarization components can also be effectively suppressed. Furthermore, we investigate the cross-correlation among the six-channel chaotic signals output from these VCSELs, and determine the region of coupled parameters for generating six-channel chaotic signals, within which satisfied is the weak cross-correlation between two signals from different VCSELs. Theoretically, the six-channel chaotic outputs can be used as physical entropy sources to generate six-channel random number sequences. By further merging the above two channel random bit sequences with weak cross-correlation, more channel random bit sequences with higher rate can be obtained. We hope this work can provide an effective guidance for multi-channel high-rate random bit generation.