To deal with the consensus problem of general first-order multi-agent systems with intermittent communication, a persistent-hold consensus algorithm is designed by introducing the hold control after the usual intermittent control. Under the fixed topology, consensus convergence conditions are obtained based on matrix theory and graph theory for the agents under our proposed persistent-hold strategy, and the results show that our proposed strategy has less conservative converging conditions than the usual intermittent control. Besides, consensus convergence conditions are also obtained for the agents under the switching topologies. Numerical simulations show the correctness of theoretical results.