This brief addresses the fixed-time leader-following attitude consensus problem for multiple spacecraft systems on a directed graph. A distributed continuous observer is designed to estimate the angular velocity of the leader within a fixed time. Based on the fixed-time observer and adding a power integrator method, a continuous distributed adaptive controller is developed to achieve the consensus tracking control in a fixed time which is regardless of the initial conditions. The proposed continuous fixed-time scheme works well when the systems are subject to model uncertainties and external disturbances. The simulation results show the effectiveness of the proposed control scheme.