Surface plasmon resonance (SPR) biosensors prepared using optical fibers can be used as a cost-effective and relatively simple-to-implement alternative to well established biosensor platforms for monitoring biomolecular interactions in situ or possibly in vivo. The fiber biosensor presented in this study utilizes an in-fiber tilted Bragg grating to excite the SPR on the surface of the sensor over a large range of external medium refractive indices, with minimal cross-sensitivity to temperature and without compromising the structural integrity of the fiber. The label-free biorecognition scheme used demonstrates that the sensor relies on the functionalization of the gold-coated fiber with aptamers, synthetic DNA sequences that bind with high specificity to a given target. In addition to monitoring the functionalization of the fiber by the aptamers in real-time, the results also show how the fiber biosensor can detect the presence of the aptamer's target, in various concentrations of thrombin in buffer and serum solutions. The findings also show how the SPR biosensor can be used to evaluate the dissociation constant (K(d)), as the binding constant agrees with values already reported in the literature.