The existing results on the leader-following attitude consensus for multiple rigid spacecraft systems assume that all the parameters of the spacecraft systems are known exactly and the information flow among the followers is bidirectional. In this paper, we remove these two assumptions. First, by introducing a new Lyapunov function, we allow the communication network to be directed. Second, we convert the leader-following consensus problem into an adaptive stabilization problem of a well defined error system. Then, under the standard assumption that the state of the leader system can reach every follower through a directed path, we further show that this stabilization problem is solvable by a distributed adaptive control law. Moreover, we also present the sufficient condition for guaranteeing the convergence of the estimated parameters to the unknown actual parameters. The existing results on the leader-following attitude consensus for multiple rigid spacecraft systems assume that all the parameters of the spacecraft systems are known exactly and the information flow among the followers is bidirectional. In this paper, we remove these two assumptions. First, by introducing a new Lyapunov function, we allow the communication network to be directed. Second, we convert the leader-following consensus problem into an adaptive stabilization problem of a well defined error system. Then, under the standard assumption that the state of the leader system can reach every follower through a directed path, we further show that this stabilization problem is solvable by a distributed adaptive control law. Moreover, we also present the sufficient condition for guaranteeing the convergence of the estimated parameters to the unknown actual parameters.