This paper describes the application of a palladium (Pd)-coated tapered optical fiber in order to develop a hydrogen (H2) sensor. A transducing channel was fabricated with multimode optical fiber (MMF) with cladding and core diameters of 125 µm and 62.5 µm, respectively, in order to enhance the evanescent field of light propagation through the fiber. The multimode optical fiber was tapered from a cladding diameter of 125 µm to a waist diameter of 20 µm, waist-length of 10 mm, and down taper and up of 5 mm, and coated with Pd using the drop-casting technique. In order to establish the palladium’s properties, various characterization techniques were applied, such as Field Emission Scanning Electron Microscopy (FESEM), Energy Dispersive X-ray (EDX), and X-ray Diffraction (XRD). The developed palladium sensor functioned reproducibly at a gas concentration of 0.125% to 1.00% H2 at room temperature in the synthetic air. In this case, the response and recovery times were 50 and 200 s, respectively. Furthermore, this study demonstrated that the production of a dependable, effective, and reproducible H2 sensor by applying a basic, cost-effective method is possible.