We report a study of semileptonic B decays to P-wave D** mesons. Semileptonic decay to D*_2 meson is observed for the first time and its product branching ratio is measured to be Br(B+ -> anti-D*0_2 l+nu) x Br(anti-D*0_2 -> D- pi+) = 0.22 +- 0.03(stat.) +- 0.04(syst.)%. The result is obtained using the fully reconstructed B tags from a data sample that contains 657 millions BB-bar pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+ e- collider.