This paper discusses Hölder's inequalities obtained through the fundamental inequality of convexity (see [1]) and presents some generalizations and complementary (or reverse) inequalities for Hölder's inequalities. Correspondingly, the conclusion on the complementary inequalities for Hölder's inequalities concerning finite series generalizes the result due to J. Aczél and E. F. Beckenbach [2]. Using the main result of this paper, we obtain some complementary inequalities for Minkowski's inequalities.