In this paper , by using critical coupling theory analysis and the finite-difference time-domain (FDTD) method for simulation calculations, we indicate theoretically that the graphene-cylinder-metal arrays structure is a perfect absorber with high-sensitivity and polarization-independent in the near-infrared region. The results show that the absorber can achieve a perfect absorption of 99.14%, which is more than 43 times the absorption of bare monolayer graphene (2.3%). In the case of the same geometric parameters, whether transverse magnetic (TM) or transverse electric (TE) polarizations, the absorption and resonance peak wavelength of the absorber are equal , because the graphene-cylinder-metal arrays structure is a highly symmetric structure. Furthermore, through numerical simulation and theoretical analysis, on the one hand, the absorber has high sensitivity up to 939.30 nm/RIU. On the other hand, when the incident light source is normally incident, the absorption performance of the arrays structure does not vary with the change of the polarization angle, that is, the system has polarization-independent characteristics. We believe this work provides a good reference for studying the interaction of enhanced light with monolayer graphene, and opens up new possibilities for the practical application of new photons and optoelectronic devices (such as detectors, sensors, etc.). By using critical coupling theory and the finite-difference time-domain (FDTD) method simulations, we indicate theoretically that the graphene-cylinder-metal arrays structure is a monolayer graphene perfect absorber in the near-infrared. Through numerical simulation and theoretical analysis, the absorber has high sensitivity up to 939.30 nm/RIU and the absorption performance of the arrays structure is polarization-independent. • The proposed graphene-cylinder-metal arrays structure can achieve a perfect absorption of 99.14%. • The sensitivity (S) and figure of merits (FOM) of the proposed perfect absorber can reach 939.30 nm/RIU and 161.11, respectively. • In the critical coupling state, the perfect absorber has high-sensitivity and polarization-independent.