Combining with the extraordinary advantages of fast-speed, label-free, high sensitivity, and real-time results, surface plasmon resonance (SPR) technology has been widely used in fields such as biochemical analysis, environmental monitoring and food safety as well as in many other aspects. In contrast to the SPR sensors utilizing the traditional noble metals (gold, silver), SPR sensors based on aluminum plasmonic have recently drawn researchers interests in these fields due to its superior features of low cost, narrow spectral bandwidth and amenability to manufacturing processes. However, aluminum exhibits the intrinsic shortcomings of bad biocompatibility and easy oxidation, which severely limit its applications. To address this problem, a surface plasmon resonance sensor based on graphene-covered aluminum nano-grating is proposed. A monolayer graphene is employed as the sensing layer that can contact directly with the molecular to be measured, because it emerged as a revolutionary two-dimensional material that shows the attractive properties of good chemical stability, large surface volume ratio, strong anti-oxidation ability, and excellent biocompatibility. Firstly, a physical model of the sensor is built based on finite element method employing COMSOL multiphysics, and the influence of the graphene layers and structure parameters of aluminum nano-grating (occupation ratio, height, and period) on the resonance spectral characteristics is investigated. Simulation results show that the coating of the graphene on the aluminum nano-grating exhibits strongly enhanced interaction between incident light and the device. Moreover, the resonance spectrum possesses the narrowest bandwidth when the aluminum nano-grating is covered by a monolayer graphene, and the reflectance of resonance spectrum is zero when the structure parameters of nano-grating are Λ=600 nm, H=40 nm and η=70%, respectively. Secondly, we further investigate the sensing characteristic of the sensor with optimized structure parameters. The results demonstrate that the sensor with a monolayer graphene covered on aluminum nano-grating obtains the highest figure of merit of 24.5 RIU-1, and the corresponding sensitivity is 626 nm·RIU-1. Such a SPR sensor with high sensitivity and good biocompatibility provides a green platform for applications in fields such as biochemical analysis, environmental monitoring and food safety monitoring.