We describe a surface plasmon resonance-based fiber sensor based on a side-polished graded-index multimode fiber, in which an Al-doped zinc oxide/gold (AZO/Au) bilayer is deposited on the side-polished surface of the fiber core to improve the detection sensitivity of the device. The AZO/Au layer is used as the active sensing member of the device with a combination of a 75-nm-thick AZO layer and a 40-nm-thick Au layer. Such a device is then applied to the concentration measurement of CH3COONa solutions, as an example showing a good response to concentration variation. The results indicate that the additional AZO layer in the active sensing member may lead to higher detection sensitivity and greater measurement stability in the measurements of solution concentration.