Using a data sample of 921.9 fb(-1) collected with the Belle detector, we study the process of e(+)e(-)-> Ds+Ds1(2536)(-) + c.c. via initial-state radiation. We report the first observation of a vector charmoniumlike state decaying to Ds+Ds1(2536)(-) + c.c. with a significance of 5.9 sigma, including systematic uncertainties. The measured mass and width are (4625.9(-6.0)(+6.2)(stat)+/- 0.4(syst))MeV/c(2) and (49.8(-11.5)(+13.9)(stat) +/- 4.0(syst)) MeV, respectively. The product of the e(+)e(-)-> Ds+Ds1(2536)(-) + c.c. cross section and the branching fraction of D-s1 (2536)(-) ->( D) over bar *0K(-) is measured from the D-s(D) over bar (s1) (2536) threshold to 5.59 GeV.