In this paper, we propose a distributed algorithm to seek the Nash equilibrium of the non-cooperative game over time-varying networks with time-varying delays. The slack block parameters, updated adaptively at each iteration, are designed to predict the players' future actions based on their current and past information. Each player then selects the appropriate slack block parameter according to the delay information and updates its local parameters accordingly. This method guarantees the convergence of the proposed algorithm, which can be proved via a non-cooperative game over a generalized delay-free network.