This paper presents a new type of microdisk resonator sensor with a gradient refractive index (GRIN) that can achieve higher sensitivity with respect to constant refractive index disks. The behavior of the microdisk resonator is simulated by 2D-FDTD method. The shift in the resonance frequency for different thicknesses of the absorbed layer and different refractive index gradients of the microdisks are studied. The best refractive index gradient function is found that leads to the largest sensitivity and smallest limit of detection. The sensitivity of a GRIN microresonator sensor (GMS) with a convex quadratic refractive index function is approximately 11 times as much as that of homogeneous microdisk sensor, which is the best record among GMSs.