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 5.9σ, including systematic uncertainties. The measured mass and width are (4625.9-6.0+6.2(stat)±0.4(syst)) MeV/c2 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 Ds1(2536)-→D∗0K-is measured from the DsDs1(2536) threshold to 5.59 GeV.