Single-mode optical fiber interferometers used with measurement or sensing systems should be stabilised to achieve high measurement accuracy and linearity in the presence of differential phase drift in their arms resulting from temperature fluctuations and other types of environmental disturbances. We propose an optical fiber interferometric measurement system which has the function of self-compensating the influences induced by the environmental disturbances and is stable and robust enough for on-line precision measurement or sensing. By employing the characteristics of fiber Bragg gratings (FBGs), the system interleaves two fiber Michelson interferometers together that share the common-interferometricoptical path. One of the fiber interferometers is used to stabilise the system while the other one is used to perform the measurement or sensing task. An electronic feedback loop for stabilising the measurement system is designed. The bandwidth of the feedback loop is 5 kHz, sufficiently wide to compensate various disturbances from environment. By these means, the system is endowed with high stability in various environments and suitability for on-line precision measurement or sensing.