Summary: Let \(G\) be a connected graph with vertex set \(V(G)\). The degree Kirchhoff index of \(G\) is defined as the sum of products between degree of all pairs of vertices and their resistance distances. The lollipop graph \(L_{n, k}\) are a class of special unicyclic graphs which come from joining an endpoint of \(P_{n-k}\) to one vertex of the cycle \(C_k\). In this paper, the authors firstly give the formula for computing the degree Kirchhoff index of \(L_{n, k}\) at first, and then characterize the extremal graphs with respect to the degree Kirchhoff index in \(L_{n, k}\).