This paper proposes a novel multi-step broadcast control (MBC) scheme to deploy a group of autonomous mobile agents for accomplishing coverage tasks in a bounded region. Traditional broadcast control (BC) schemes use a one-to-all communication framework to transmit a uniform signal to all agents, making it cost-effective compared with any all-to-all communication-based scheme for a multi-agent system. However, as BC schemes are based on a single-step view of the environment for decision-making, the environment’s varying distribution density is not known immediately to the agents, resulting in suboptimal performance. To overcome this drawback, this paper proposes an MBC scheme, where agents use a predictive multi-step view and are able to detect the varying densities in the environment ahead of time. The local controller output is estimated using a weighted averaging technique which assigns a higher weight to immediate steps; this feature compensates for any decrease in prediction accuracy as the number of steps increases. We demonstrate the effectiveness of the proposed MBC scheme using a coverage task over a region with uneven population density. Compared to existing BC schemes, the proposed MBC scheme shows superior convergence characteristics in task accomplishment and deployment efficiency.