In this paper, we study spectrum trading in cognitive radio (CR) networks with multiple primary services (PSs) and multiple secondary services (SSs) from a game-theoretic perspective. We propose a multistage Bayesian game-based trading model which accounts for unknown private information of players (for example, the number of user connections in PSs may be unknown to the SSs) as in practical network scenarios. The perfect Bayesian equilibrium (PBE) is derived by solving an involved sequential optimization problem. We formulate the joint Karush-Kuhn-Tucker (KKT) conditions and use the KKT translation technique to obtain the PBE at each stage. Simulation demonstrates the convergence of the sequence of strategies in the multistage Bayesian game.