A new design of a fiber optic Surface Plasmon Resonance (SPR) sensor using Palladium as a sensitive layer for hydrogen detection is presented. In this approach, a transducer layer is deposited on the outside of a multimode fiber, after removing the optical cladding. The transducer layer is a multilayer stack made of a Silver, a Silica and a Palladium layer. The spectral modulation of the light transmitted by the fiber allows to detect the presence of hydrogen in the environment. The sensor is only sensitive to the Transverse Magnetic polarized light and the Traverse Electric polarized light can be used therefore as a reference signal. A more reliable response is expected for the fiber SPR hydrogen sensor based on spectral modulation instead of on intensity modulation. The multilayer thickness defines the sensor performance. The silica thickness tunes the resonant wavelength, whereas the Silver and Palladium thickness determine the sensor sensitivity. In an optimal configuration (NA = 0.22, 100 ?m core radius and transducer length = 1 cm), the resonant wavelength is shifted over 17.6 nm at a concentration of 4% Hydrogen in Argon for the case of the 35 nm Silver/ 100 nm Silica/ 3 nm palladium multilayer.