In this paper, the production of the charged Higgs pair associated with the Z(0) boson is analyzed in the minimal extension of the standard model, the so-called two-Higgs-doublet model. The process e(+)e(-) -> H(+)H(-)Z(0) is calculated at the tree level including all the possible diagrams in the two-Higgs-doublet model. The numerical analysis is performed in consideration of the current experimental constraints and various scenarios for the free parameters of the model. The results are presented as a function of the center-of-mass energy, the charged Higgs mass (m(H +/-)), and the ratio of the vacuum expectation values (t ss). The unpolarized cross section, taking into account the results in the flavor physics, gets up to 0.278 fb for m(H +/-) = 175 GeV, and it declines with decreasing m(H +/-) in type I. However, it gets down to 0.073 fb for m(H +/-) = 500 GeV in type II. Further, the calculation is also carried out in the nonalignment scenario and low-m(h)0 scenario. The effect of the polarized incoming e(+) and e(-) beams shows that the cross section is enhanced by a factor up to 2.5 at P(+0.60, -0.80thorn polarization configuration. Decay channels of the charged Higgs, possible final states of the process, and some differential distributions belonging to the charged Higgs and Z(0) boson are examined for each scenario. The analysis shows that some channels have a higher branching ratio such as H+ t (b) over bar, H+ -> W(+)h(0), and H+ -> (W+H0). These decay channels are essential in the charged Higgs searches at the lepton colliders for the scenarios interested. The detection of the charged Higgs is a powerful sign for the extended scalar sectors, and the results show the potential of a future lepton collider.