The precise determination of the CKM matrix element |Vcb| is important for carrying out tests of the flavour sector of the Standard Model. In this article we present a preliminary analysis of the B¯0→D∗+ℓ−ν¯ℓ decay mode and its charge conjugate, selected in events that contain a fully reconstructed B-meson, using 772 million e+e−→Υ(4S)→BB¯ events recorded by the Belle detector at KEKB. Unfolded differential decay rates of four kinematic variables fully describing the B¯0→D∗+ℓ−ν¯ℓdecay in the B-meson rest frame are presented. We measure the total branching fraction (B¯0→D∗+ℓ−ν¯ℓ)=(4.95±0.11±0.22)×10−2, where the errors are statistical and systematic respectively. The value of |Vcb| is determined to be (37.4±1.3)×10−3. Both results are in good agreement with current world averages.