Recent years have witnessed a rapid increase in online data volume and the growing challenge of information overload for web use and applications. Thus, information diversity is of great importance to both information service providers and users of search services. Based on a diversity evaluation measure (namely, information coverage), a heuristic method—FastCovC+S-Select—with corresponding algorithms is designed on the greedy submodular idea. First, we devise the CovC+S-Select algorithm, which possesses the characteristic of asymptotic optimality, to optimize information coverage using a strategy in the spirit of simulated annealing. To accelerate the efficiency of CovC+S-Select, its fast approximation (i.e., FastCovC+S-Select) is then developed through a heuristic strategy to downsize the solution space with the properties of information coverage. Furthermore, ample experiments have been conducted to show the effectiveness, efficiency, and parameter robustness of the proposed method, along with comparative analyses revealing the performance’s advantages over other related methods.