The information society has spawned the right to be forgotten, and its extension in criminal justice has produced the criminal right to be forgotten. The criminal right to be forgotten should be strictly restricted. The study of the obligation of the criminal right to be forgotten is of great significance for understanding that right. The subjects of the obligation corresponding to the criminal right to be forgotten include the state organs, the news media and the public. The statutory conditions for fulfilling the corresponding obligations refer to making the uses of personal data illegal or unreasonable out of objective or subjective reasons or with the special protection of the law. The types of obligations include positive and negative obligations, in which positive obligations are mainly sealing and deleting data, and negative obligations include refusing to collect, store or transmit data. The performance of the corresponding obligations shall be subject to specific procedures, including the application by the subjects of right, the court review and judgment, and the performance by the subjects of obligation. To ensure that the subjects of obligation fulfill their corresponding obligations, liabilities for violation of law shall be set up for refusing to perform obligations, such as civil liability, criminal liability, legal liability of the administrative organ and its staff, and state compensation liability.