In many real-world problems and applications, finding only a single element, even though the best, among all possible candidates, cannot fully meet the requirements. We may wish to have a collection where each individual is not only outstanding but also distinctive. Diversified Top-k (DTk) problems are a kind of combinatorial optimization problem for finding such a promising collection of multiple sub-structures, such as subgraphs like cliques and social communities. In this paper, we address two representative DTk problems, DTk Clique search (DTkC) and DTk Weight Clique search (DTkWC), and propose a novel and effective algorithm called Diversified Top-k Evolutionary AlgorithM (DiverTEAM) for the two problems. DiverTEAM consists of a local search algorithm, which focuses on generating high-quality and diverse individuals and sub-structures, and a genetic algorithm that makes individuals work as a team and converge to (near-)optima efficiently. Extensive experiments show the excellent and robust performance of DiverTEAM across various benchmarks of DTkC and DTkWC.