In this paper, we propose a novel Adaptive Discriminant Analysis for semi-supervised feature selection, namely SADA. Instead of computing fixed similarities before performing feature selection, SADA simultaneously learns an adaptive similarity matrix S and a projection matrix W with an iterative method. In each iteration, S is computed from the projected distance with the learned W and W is computed with the learned S. Therefore, SADA can learn better projection matrix W by weakening the effect of noise features with the adaptive similarity matrix. Experimental results on 4 data sets show the superiority of SADA compared to 5 semisupervised feature selection methods.