A microwave-photonic low-coherence interferometry (MPLCI) system is proposed for fully distributed optical fiber sensing. Assisted by an unbalanced Michelson interferometer, a low-coherence laser source is used to interrogate cascaded Fabry-Perot interferometers along with an optical fiber for a dark zone free (or spatially continuous) distributed measurement. By combining the advantages of microwaves and photonics, the MPLCI system can synergistically achieve high sensitivity and high spatial resolution. Our tests have confirmed a strain resolution of 95 nε at the spatial resolution of 10 cm.