A surface acoustic wave (SAW)-based hydrogen sensor and its corresponding interface electronics have been developed to measure the hydrogen concentration in air at room temperature. Two SAW delay lines with center frequencies of 284 and 284.3 MHz are employed for the sensor system to eliminate any environmental disturbances emerging from temperature and humidity variations on a sensor output. A beehive-configured and Cu-doped SnO2 nanostructure is used as a hydrogen-sensitive material to have a high surface to volume ratio, high sensitivity, and selectivity for the target hydrogen. The smallest frequency difference detectable in our sensor system including oscillator, mixer, low pass filter, comparator, and field programmable gate array (FPGA) was ≈1 Hz, which is a significant output value that can sufficiently detect hydrogen concentrations below 1 ppm. Compared with pure SnO2, 3D Cu (3%)-doped SnO2 nanostructure based-SAW sensor exhibited the highest response to hydrogen gas. The elevated response of the 3D Cu-doped SnO2 based SAW sensor to hydrogen gas is mainly attributed to the acoustoelectric interaction. Photoluminescence and X-ray photoelectron spectroscopy analysis divulged that Cu-doping in SnO2 produces a large number of surface oxygen vacancies, which enhances the hydrogen adsorption on the SnO2 surface, resulting in a significant improvement in the response to hydrogen gas. The sensor characteristics at the system level showed excellent selectivity, repeatability, and long-term stability to hydrogen gas. The sensing mechanisms (mass loading and acoustoelectric interaction) in the SAW sensor due to hydrogen adsorption have been experimentally investigated and the obtained results are discussed in detail.