Fuzzy rough set theory has been paid much attention since it can be used to deal with the uncertainty in the real-valued data or even the mixed data. One of the most important applications of fuzzy rough sets is feature selection, and there have existed many related feature selection methods. However, little attention has been paid on fast feature selection algorithms. Data collected in practice generally include noises or possess some instances with less information. Considering to previously select representative instances from the original data set and perform data mining algorithms on the selected instances set, one may reduce the computation of the algorithms. In view of the advantage of instance selection, the instances are firstly selected based on fuzzy rough sets according to the values of the fuzzy lower approximation of instances in this paper. Then, the evaluation measure of feature selection is constructed by using fuzzy rough set-based information entropy of the selected instances, and the corresponding feature selection algorithm is provided to alleviate the computational complexity. Some numerical experiments are conducted to show the efficiency of the proposed fast algorithm, and the reasonable suggestion of the critical parameter is given to determine the number of the selected instances.