In this paper, a system security problem is studied based on a two-person non-cooperative dynamic game. Security of the system is regarded in the context of observability. Namely a system is secure if it is not observable. Both the defender and attacker are assumed to have means to modify the dimension of unobservable subspace, which is set as the value function. The strategies and algorithms to minimize or maximize the value function are given respectively. Finally, examples are provided to demonstrate the effectiveness of the proposed algorithms and show some interesting game results, including accumulation mode, loop mode and locked mode.