Recently, eigenvoice approach has been widely used for rapid speaker adaptation. However, even in the eigenvoice approach, Performance improvement using very small amount of adaptation data is relatively small in comparison with that using somewhat large adaptation data because the reliable estimation of weights of eigenvoice is difficult. In this paper, we propose a rapid speaker adaptation method based on eigenvoice using the weight distribution characteristics to improve the performance on a small adaptation data. In the Experimental results on vocabulary-independent word recognition task (using PBW 452 database), the weight threshold method alleviates the problem of relatively low performance for a tiny small adaptation data. When single adaptation word is used, word error rate is reduced about 9-18% by the weight threshold method.