Inspired by the efficient proof procedures discussed in Computability logic [3],[5],[6], we describe a heuristic proof procedure for first-order logic. This is a variant of Gentzen sequent system [2] and has the following features: (a) it views sequents as games between the machine and the environment, and (b) it views proofs as a winning strategy of the machine. From this game-based viewpoint, a poweful heuristic can be extracted and a fair degree of determinism in proof search can be obtained. This article proposes a new deductive system LKg with respect to first-order logic and proves its soundness and completeness.