As the foundation of routing, topology control should minimize the interference among nodes, and increase the network capacity. With the development of mobile ad hoc networks (MANETs), there is a growing requirement of quality of service (QoS) in terms of delay. In order to meet the delay requirement, it is important to consider topology control in delay constrained environment, which is contradictory to the objective of minimizing interference. In this paper, we focus on the delay-constrained topology control problem, and take into account delay and interference jointly. We propose a cross-layer distributed algorithm called interference-based topology control algorithm for delay-constrained (ITCD) MANETs with considering both the interference constraint and the delay constraint, which is different from the previous work. The transmission delay, contention delay and the queuing delay are taken into account in the proposed algorithm. Moreover, the impact of node mobility on the interference-based topology control algorithm is investigated and the unstable links are removed from the topology. The simulation results show that ITCD can reduce the delay and improve the performance effectively in delay-constrained mobile ad hoc networks.