Based on 7.33 fb(-1) of e(+)e(-) collision data collected by the BESIII detector operating at the BEPCII collider at center-of-mass energies from 4.128 to 4.226 GeV, a search for the Majorana neutrino nu(m) is conducted in the lepton-number-violating decays of D-s(+) -> h(-)h(0)e(+)e(+). Here, h(-) represents a K- or pi(-), and h(0) represents a pi(0), K-S(0) or phi. No significant signal is observed, and the upper limits of their branching fractions at the 90% confidence level are determined to be B(D-s(+) -> phi pi(-)e(+)e(+)) < 6.9 x 10(-5), B(D-s(+) -> phi K(-)e(+)e(+)) < 9.9 x 10(-5), B(D-s(+)-> K-S(0)pi(-)e(+)e(+)) < 1.3 x 10(-5), B(D-s(+) -> K(S)(0)K(-)e(+)e(+)) < 2.9 x 10(-5), B(D-s(+) -> pi(-)pi(0)e(+)e(+)) < 2.9 x 10(-5) and B(D-s(+) -> K-pi(0)e(+)e(+)) < 3.4 x 10(-5). The Majorana neutrino is searched for with different mass assumptions within the range [0.20, 0.80] GeV/c(2) in the decay of D-s(+) -> phi e(+)nu(m) with nu(m) -> pi(-)e(+), and the upper limits of the branching fractions at the 90% confidence level are at the level of 10(-5)-10(-2), depending on the mass of the Majorana neutrino.