Tilted fiber Bragg grating (TFBG) sensors are widely used in biochemical and electrochemical sensing due to their high sensitivity to refractive index (RI) of the surrounding medium. Ability of TFBGs to measure small RI change is currently limited due to the discrete spectral characteristics of TFBG cladding modes. Here we propose a method to measure both small and large RI changes with high accuracy and sensitivity by measuring the derivative of the intensity of the entire cladding mode envelope. The peak of the derivative curve provides a continuous and linear response to the RI change, which overcomes the problem of 'cut-off mode hopping' that, until now, has limited the resolution of RI measurement using TFBGs. Experimental results demonstrate that, for small RI change (less than 0.002 RIU), the cladding envelope derivative method improves the interrogation sensitivity from tens of nm/RIU (using cut-off mode) to hundreds of nm/RIU (this method) together with a linear response (better than 98%). Moreover, such method provides the ability of temperature-crosstalk calibration, offering a powerful new tool for biochemical detection.