In this work, the consensus of networked agents under denial-of-service (DoS) attacks is studied. Due to DoS attacks, communication channels would be intermittently congested, which inevitably affects state update. This situation has been recast into a consensus problem with on off control by others, assuming undirected topology and periodic DoS attacks. Obviously, these assumptions may fail, and hence, aperiodic attacks and directed topology are considered here. Our theoretical results reveal that consensus is achievable when the time average of the DoS attack duration is upper bounded. The new consensus criterion also demonstrates better generality and tractability. Finally, simulation results are presented.