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For a class of discrete-time singular Markov jump systems with an event-triggered mechanism, the problem of asynchronous fault detection filtering is solved. First, an event-triggered strategy is proposed to achieve the purpose of rationally using network resources and reducing the burden of communication. Then, considering the asynchronous phenomenon between the system mode and the filter mode, two different Markov chains are used to represent the system mode and the filter mode respectively, and on this basis, a design method of the asynchronous fault detection filter (FDF) is proposed. Next, by combining the design problem of the asynchronous fault detection filter with the event-triggered mechanism, based on the Lyapunov stability theory, the sufficient condition is given to ensure that the residual error system is to be regular, causal, stochastically stable and satisfy performance. The expected parameters of the asynchronous fault detection filter are available by solving a specific set of linear matrix inequality (LMI). Finally, a simulation example is given to illustrate that the design method of the asynchronous fault detection filter is effective.