This paper is concerned with the derivation of open-loop Stackelberg (OLS) solutions of a class of continuous-time two-player nonzero-sum differential games characterized by quadratic cost functionals and linear singular systems. By applying the calculus of variations, necessary conditions are derived under which the open-loop Stackelberg solution of the leader exists. Under the transformation by which the matrix E has diagonal form, we derive a matrix Riccati differential equation from the necessary conditions. An example is given to illustrate the results of the paper.