A scheme of classical-quantum signal transmission in a shared fiber is proposed based on a measurement-device-independent protocol. The counting rate formula of spontaneous Raman scattering noise is deduced and the effects of the incident power of classical signals, channel number of quantum signals and average photon numbers of quantum signals on the quantum key distribution (QKD) performances are analyzed. The numerical simulation results show that the maximum safe transmission distance for the QKD by the proposed scheme is up to 141 km when the incident power of classical signals is 0 dBm (i.e., the communication capacity of 84.8 Gbit/s). Even when the incident power increases to 11 dBm (i.e., the communication capacity of 1.068 Tbit/s), it is still up to 100 km. Compared with the existing optimal transmission scheme, the maximum safe transmission distance of the QKD by the proposed scheme is extended by 26 km. Although the QKD performance decreases with the increase of the incident power of classical signals, the performance can be compensated by the multiplexing channels of quantum signals and the optimization of the average photon numbers of quantum signals.