Machine unlearning is a complex process that necessitates the model to diminish the influence of the training data while keeping the loss of accuracy to a minimum. Despite the numerous studies on machine unlearning in recent years, the majority of them have primarily focused on supervised learning models, leaving research on contrastive learning models relatively underexplored. With the conviction that self-supervised learning harbors a promising potential, surpassing or rivaling that of supervised learning, we set out to investigate methods for machine unlearning centered around contrastive learning models. In this study, we introduce a novel gradient constraint-based approach for training the model to effectively achieve machine unlearning. Our method only necessitates a minimal number of training epochs and the identification of the data slated for unlearning. Remarkably, our approach demonstrates proficient performance not only on contrastive learning models but also on supervised learning models, showcasing its versatility and adaptability in various learning paradigms.