Mild cognitive impairment (MCI) is a pre-existing state of Alzheimer's disease (AD). An accurate prediction on the conversion from MCI to AD is of vital clinical significance for potential prevention and treatment of AD. Longitudinal studies received widespread attention for investigating the disease progression, though most studies did not sufficiently utilize the evolution information. In this paper, we proposed a cerebral similarity network with more progression information to predict the conversion from MCI to AD efficiently. First, we defined the new dynamic morphological feature to mine longitudinal information sufficiently. Second, based on the multiple dynamic morphological features the cerebral similarity network was constructed by sparse regression algorithm with optimized parameters to obtain better prediction performance. Then, leave-one-out cross-validation and support vector machine (SVM) were employed for the training and evaluation of the classifiers. The proposed methodology obtained a high accuracy of 92.31% (Sensitivity = 100%, Specificity = 82.86%) in a three-year ahead prediction of MCI to AD conversion. Experiment results suggest the effectiveness of the dynamic morphological feature, serving as a more sensitive biomarker in the prediction of MCI conversion.