The centromere drive model explaining rapid evolution of eukaryotic centromeres predicts higher frequency of positive selection acting on centromeric histone H3 (CenH3) in clades with asymmetric meiosis compared to the clades with only symmetric meiosis. However, despite the impression one might get from the literature, this key prediction of the centromere drive model has not only never been confirmed, but it has never been tested, because all the previous studies dealt only with the presence or absence instead of the frequency of positive selection. To provide evidence for or against different frequencies of positively selected CenH3 in asymmetrics and symmetrics, we have inferred the selective pressures acting on CenH3 in seventeen eukaryotic clades, including plants, animals, fungi, ciliates and apicomplexa, using codon-substitution models, and compared the inferred frequencies between asymmetrics and symmetrics in a quantitative manner. We have found that CenH3 has been evolving adaptively much more frequently in clades with asymmetric meiosis compared with clades displaying only symmetric meiosis which confirms the prediction of centromere drive model. Our findings indicate that the evolution of asymmetric meiosis required CenH3 to evolve adaptively more often to counterbalance the negative consequences of centromere drive.