The consensus tracking problem of leader-follower multi-agent systems (MASs) with singular structures on jointly connected topology is studied in this paper. To achieve the objective of consensus tracking, a distributed adaptive control protocol is formulated to adjust the coupling weights among the agents using the adaptive rate, where the adaptive protocol can be implemented by each agent in a fully distributed manner without using any global information. A fuzzy logic system method is used to deal with the nonlinear terms in response to the limitations of nonlinear system analysis. The consensus tracking problem is transformed into an error system stability analysis, and two sufficient conditions are provided to guarantee the control objective based on Lyapunov stability theory and singular system theory. Finally, the effectiveness of this method is verified through a simulation example.