This article introduces a new type of graphene-based perfect absorber that features tunability across four wave peaks and high sensitivity, consisting of Ag–SiO2–graphene. By controlling the Fermi level and relaxation time of graphene, the tunability of the absorber is achieved, and by changing the refractive index of SiO2, the selectivity of the resonant wavelength is realized. The results show that the absorber has an average absorption rate of 98.54% at four wavelengths: 2092.24 nm, 2180.67 nm, 2230.08 nm, and 2336.17 nm. The electric field distribution intensity is simulated to verify whether it meets the impedance matching theory, exploring the physical mechanism behind the high absorption rates at these four peaks. Different polarizations and inclined incidence angles are investigated to explore the absorber's insensitivity to polarization, demonstrating excellent insensitivity within an inclination angle range from 0° to 65°. The sensitivities of the four peaks are 501.54 nm RIU−1, 565.76 nm RIU−1, 605.47 nm RIU−1, and 582.70 nm RIU−1, respectively. Finally, the practical application of the absorber in detecting aqueous solutions of 10%, 20%, 25% glucose solutions, and 30%, 50% sugar solutions is simulated, and the results show that the absorber has good sensing performance. This paper's absorber features four-peak perfect absorption and excellent tilt insensitivity, good refractive index sensitivity, and holds great potential applications in detectors and optical communication systems.