In this work, the development and testing of a novel fiber-optic based label-free biosensor is presented, whose performance were verified through the detection of C-reactive protein (CRP) in serum. The device is based on a long period grating fabricated in a double cladding fiber with a W-shaped refractive index (RI) profile. As a result, the working point of the device was tuned to the mode transition region by chemical etching of the outer fiber cladding, obtaining a significant enhancement of the RI sensitivity and an excellent visibility of the grating resonances due to the mode transition in an all-silica structure. The fiber transducer was coated with a nanometric thin layer of graphene oxide in order to provide functional groups for the covalent immobilization of the biological recognition element. A very low limit of detection of about 0.15 ng/mL was obtained during the detection of CRP in serum, and a large working range (1 ng/mL – 100 μg/mL) of clinical relevance has been also achieved.