Summary: Let \(W=\text{span}_C\{M_r|r\in Z\}\) denote the rank-one Witt algebra with the bracket: \([M_r, M_s]=(s-r)M_{r+s}\). Let \(V=\text{span}_C\{N_s|s\in Z\}\) be a vector space which can be regarded as \(W\)-module in the sense of \(M_r\). \(N_s=sN_{r+s}\). Let \(G\) be the split extension of Witt algebra by its module \(V\). The universal central extension of \(G\) is investigated.