Case Amplification can improve the accuracy of a collaborative filtering (CF) algorithm with no extra space overhead by amplifying the effect of close candidates in the prediction. However, in a cold start scenario, the traditional Case Amplification on an item-based prediction can reduce accuracy. Given a small known set, Case Amplification can give a mediocre candidate an unsuitable amplification, by amplifying the numerator and the denominator in a predicting formula equally. We propose a skew amplification mechanism to address the problem: we amplify the numerator and the denominator differently. This reduces the effect of a mediocre but close item in the prediction. The balance between different amplifications is kept automatically by a controller, whose behavior depends on the size of the given set. Evaluation was carried out on four benchmarks, and results show that, in a cold-start scenario, skew amplification outperforms Case Amplification on boosting an item-based CF algorithm, especially when the given set becomes small.