The master equation of the single-electron triple-barrier tunnel-junction(TBTJ) model is developed based on the orthodox theory. The steady distribution of electrons on the Coulomb islands is obtained with the linear system of equations method and the I-V curves through the simulation method are presented in this paper. Discontinuities of the slope of the curve at the flat-form of Coulomb staircase compared to double barrier tunnel-junction system, which is caused by the change of the electron numbers on the second Coulomb island, are found. The system temperature requirement can be reduced in the TBTJ system, and the maximum temperature at which Coulomb staircase can be resolved is estimated using the energy spacing at the Fermi energy.