We report a miniature hydrogen sensor that consists of a subwavelength diameter tapered optical fiber coated with an ultra thin palladium film. The optical properties of the palladium layer changes when the device is exposed to hydrogen. Consequently, the absorption of the evanescent waves also changes. The sensor was tested in a simple light transmission measurement setup that consisted of a 1550 nm laser diode and a photodetector. Our sensor is much smaller and faster than other optical hydrogen sensors reported so far. The sensor proposed here is suitable for detecting low concentrations of hydrogen at normal conditions.