The coherent quantum transport is investigated in normal-metal/superconductor/normal-metal (N/S/N) double tunnel junctions under a Zeeman magnetic field on the S. Taking simultaneously into account the electron-injected current from one N electrode and the hole-injected current from the other N electrode, we derive a general formula for the differential conductance in the N/S/N system. It is shown that the conductance spectrum exhibits oscillatory behaviour with the bias voltage, and the oscillation amplitude is reduced with increasing temperature and Zeeman magnetic field, the Zeeman energy can lead to the Zeeman splitting of conductance peaks. In the tunnel limit, a series of bound states of quasiparticles will form in the S.