This article investigates the dynamic consensus problem for the discrete-time second-order integrator networked multiagent system with time-varying delay and switching topology, in which the speed of each agent is not required to be synchronized to zero value. Novel consensus protocols using only relative state information are proposed, and sufficient conditions for dynamic consensus are derived. The results show that consensus can be reached for both the case with delay and the case without delay, if the gain is sufficiently small and the union of interaction graphs is scrambling or contains a spanning tree frequently enough as the system evolves. Numerical examples demonstrate the effectiveness of the theoretical results.