This paper is to investigate the main thoughts and arguments of act utilitarianism and rule utilitarianism. It is pointed out that both act utilitarianism and rule utilitarianism fail to provide sufficient underpinnings for the condition of moral dilemmas when we feel the need to rely on moral judgments and take action. It is concluded that despite the principle of the pursuit of the greatest happiness of the greatest number, utilitarianism cannot assure that each individual can own the greatest satisfaction and happiness, given that it is meant to sacrifice the benefits of some individuals.