Analyzing e(+)e(-) collision data corresponding to an integrated luminosity of 7.33 fb(-1) collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector, we measure the branching fraction of the semileptonic decay D-s(+) -> K(0)e(+) nu(e) to be (2.98 +/- 0.23(stat) +/- 0.12(syst)) x 10(-3). Based on fit to the partial decay rates in various q(2) intervals, the product value of D-s(+) -> K-0 hadronic form factor and Cabibbo-Kobayashi-Maskawa element is measured to be f(+)(K0)(0)vertical bar V-cd vertical bar = 0.143 +/- 0.011(stat) +/- 0.003(syst). With vertical bar V-cd vertical bar = 0.22486 +/- 0.00067 as an input, the hadronic form factor is evaluated to be f(+)(K0) = 0.636 +/- 0.049(stat) +/- 0.013(syst). The branching fraction and form factor measurements are factors of 1.6 and 1.7 more precise than the previous world averages, respectively.