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In 2008, Rump et al. developed algorithms for accurate floating-point summation. In particular, the algorithm AccSum, which provides a faithfully rounded result in working precision of the exact sum of given floating-point numbers, is known to be a very fast algorithm for this purpose. In this talk an acceleration method for AccSum is proposed. The method utilizes a simple technique of grouping given data with the algorithm FastTwoSum for summation of two floating-point numbers as the accumulator. The computational cost for the proposed method can be much smaller than that for AccSum, though it strongly depends on given data. Numerical results are presented for illustrating the effectiveness of the proposed algorithm.