Multicast is an important way to diffuse data in duty-cycled wireless sensor networks (WSNs), where nodes can receive data only in active state. The communication delay can be extremely large if inappropriate schedules are adopted. Unfortunately, most previous methods do not consider controlling multicast delay energy-efficiently. This paper studies the minimum active time slot augmentation for delay-bounded multicast (MAADM) problem in duty-cycled WSNs. The MAADM problem is proved to be NP-hard even under the node-exclusive interference model. An optimal algorithm is proposed for the MAADM problem when K = 2 and a heuristic latency bounding algorithm is proposed for source-to-all communications, where K denotes the number of the destination nodes. When K > 2, two (K-1)-approximation algorithms are designed for the MAADM problem. In addition, a low computation-complexity distributed algorithm is proposed. To the best of our knowledge, this is the first work that develops a series of efficient centralized and distributed algorithms for the MAADM problem in dutycycled WSNs. The theoretical analysis and experimental results verify that all the proposed algorithms have high performance in terms of delivery delay and energy consumption.