The fiber Bragg grating (FBG) sensor is well known for simple fabrication, absolute measurement, inherent multiplexing capability, etc. To date, most FBG sensors that use a broadband light source for demodulation can only achieve resolution at the µɛ level. In this Letter, we propose a white-light-driven self-reference sensing system with FBGs, using a Mach-Zehnder interferometer (MZI) and a white light source, to realize multiplexed high-resolution vibration sensing with a very simple system configuration. A strain resolution of 35p ε/Hz at 1 kHz is demonstrated, which is several orders of magnitude better than the current FBG sensor systems with white light sources. The performance of the sensing system is analyzed, and multiplexing capability is also experimentally evaluated; there is no observable cross talk.