In this paper, we study the Distributed Maximization problem in the number-in-hand coordinator model. In this model, a central coordinator communicates with k sites, each of which holds a private integer, and the task of the coordinator is to output the maximum number among these integers. We propose two randomized algorithms to solve this problem effectively, achieving communication complexity of \(O(k\log \log N+ \log N)\) bits. In addition, we provide a tight lower bound which shows the optimality of our algorithms.