As a feature selection technique in rough set theory, attribute reduction has been extensively explored from various viewpoints especially the aspect of granularity, and multi-granularity attribute reduction has attracted much attention. Nevertheless, it should be pointed out that multiple granularities require to be considered simultaneously to evaluate the significance of candidate attribute in the corresponding process of computing reduct, which may result in high elapsed time of searching reduct. To alleviate such a problem, an acceleration strategy for neighborhood based multi-granularity attribute reduction is proposed in this paper, which aims to improve the computational efficiency of searching reduct. Our proposed approach is actually realized through the positive approximation mechanism, and the processes of searching qualified attributes are executed through evaluating candidate attributes over the gradually reduced sample space rather than all samples. The experimental results over 12 UCI data sets demonstrate that the acceleration strategy can provide superior performance to the naive approach of deriving multi-granularity reduct in the elapsed time of computing reduct without generating different reducts.