This letter reports telecom-band sequential time-bin entangled photon-pair generation at a repetition rate of 10 GHz in periodically poled reverse-proton-exchange lithium niobate waveguides based on mode demultiplexing. With up-conversion single-photon detectors, we observed an entangled-photon-pair flux of 313 Hz and a two-photon-interference-fringe visibility of 85.32% without subtraction of accidental noise contributions.