We present the wavelength (λ)-independent ultimate and maximum angular sensitivity of a grating surface plasmon resonance sensor, as long as the grating of metal has much higher permittivity than analyte (na2). For 1.32≤n(a)≤1.36, the maximum angular sensitivity reaches 493.7 (535.9)°/RIU by the single (double)-dip method. The real Al-based sensor in an optimal structure for a high figure of merit exhibits higher sensitivity but narrower reflection dip when working at a longer wavelength, and the real sensitivity increases from 292.5 (344.5) to 338.0 (396.3)°/RIU at respective λ=0.85 and 1.55 μm before the metal oxidation. After the oxidization, the sensitivity is degraded by ≤3.2% (2.8%), and the detection error of δn(a)≤1.3e-3 (1.1e-3) is introduced to the sensor working at near-infrared wavelengths of interest.