In this talk, we consider a two-person zero-sum linear-quadratic stochastic differential game. By combining the notion of Elliott and Kalton’s non-anticipative strategy and the classical feedback mechanism, we establish a thoroughly closed-loop formulation for the game. A saddle point in the form of strategy laws is constructed based on the solution of a Riccati equation. A key part of our analysis involves proving the global solvability of this Riccati equation, which is interesting in its own right. Moreover, we demonstrate an indefinite phenomenon arising from the linear-quadratic game.