Imposing lenient punishments on those confessing their crimes and accepting punishments in criminal cases can be treated first as a criminal policy,and then as a system which is applicable to all criminal procedures,including investigation,examination and prosecution,trial and execution. The process of confessing their crimes and accepting punishments is the process of expressing apology,which reveals the connotations of confessing crimes and accepting punishments in the theory of apology. Confessing their crimes include the following: they should make a confession of their crimes,state clearly the process of their violations,and promise not to commit any crime again. Accepting punishment include their acceptance of the bad results of the crime and give compensations for the victims and their families. The lenient punishments include lighter criminal compulsory measures,simplified procedures of investigation,prosecution and judgment,the end of the legal procedure in advance or a more lenient sentence.