In this article, a multiple-node fiber-optic time synchronization scheme is proposed over a hybrid star and bus-shaped optical fiber network based on the bidirectional wavelength division multiplexing (BWDM) transmission. Time signals can be obtained at arbitrary access and remote nodes, which are accurately synchronized with the one at the local node by compensating for the transmission delay of corresponding fiber link. By utilizing the optimized wavelengths configuration, in addition to eliminating the impact of single Rayleigh backscattering of the optical fiber, the effect of bidirectional wavelengths asymmetry on the accuracy of time synchronization is also effectively suppressed. Therefore, link calibrations are not required in the proposed scheme. Experimentally, a multiple-node time synchronization system is demonstrated over a hybrid star and bus fiber network with three branches. The results show that the stabilities in terms of time deviation (TDEV) of less than 30 ps at 1 s and 5 ps at 10000 s can be obtained for all of the access and remote nodes, and the clock difference of less than 25 ps can be achieved.