Hydrogen gas sensors, based on palladium membranes, have considerable applications in areas such as industry, aerospace, and green energy monitoring. In this paper, we propose a surface plasmon resonance nanosensor, in which the main metal sensor is taken to be gold with a thin nanolayer of palladium membrane. The reason we chose palladium is its exceptional property of having high permittivity to hydrogen penetration. In this paper, formation of palladium hydride (PdH$_{x}$, where x = H / Pd) is achieved and simulation is provided using Materials Studio software. Based on an intermediate assumption, a semiconductor gold composite layer is used instead of gold, because the composite layer gives higher efficiency. In the final structure, twelve alternating layers of gold and silicon are used (silicon and gold with thicknesses of 0.53 and 13.6 nm, respectively). The proposed structure is simulated under carbon monoxide exposure to analyze its cross-sensitivity to other gases. Finally, the sensor shows higher sensitivity and narrower linewidth under hydrogen exposure compared to carbon monoxide exposure.