In general, there are two kinds of cooperative driving strategies, planning-based strategy, and ad hoc negotiation-based strategy, for connected and automated vehicles merging problems. The planning-based strategy aims to find the globally optimal passing order, but it is time-consuming when the number of considered vehicles is large. In contrast, the ad hoc negotiation-based strategy runs fast, but it always finds a locally optimal solution. In this paper, we propose a grouping-based cooperative driving strategy to make a good tradeoff between computation time and coordination performance. The key idea is to fix the passing orders for some vehicles whose inter-vehicle headways are small enough (e.g., smaller than the pre-selected grouping threshold). From the viewpoint of optimization, this method reduces the size of the solution space. Then, two analyses are given to explain why this kind of strategy is good and how to determine suitable values for the strategy parameters. A series of simulation experiments are carried out to validate that the proposed strategy can yield a satisfied coordination performance with less computation time and is promising to be used in practice.