Subgame Perfect Equilibrium (SGPE) is a refined version of Nash equilibrium used in games of sequential nature. Computational complexity of classical approaches to compute SGPE grows exponentially with the increase in height of the game tree. In this paper, we present a quantum algorithm based on discrete-time quantum walk to compute Subgame Perfect Equilibrium (SGPE) in a finite two-player sequential game. A full-width game tree of average branching factor b and height h has nodes in it. The proposed algorithm uses oracle queries to backtrack to the solution. The resultant speed-up is times better than the best known classical approach, Zermelo's algorithm.