In practice, alarms configured for steady operating states often become a nuisance during the start-up operation of industrial equipment. As a result, they not only distract plant operators, but may also cause worse consequences, such as pump trips. Motivated by such as a practical problem, this paper presents a new alarm monitoring method for equipment start-up operations. The proposed method is capable of preventing nuisance alarms as well as achieving effective alarm monitoring during equipment start-ups. The contributions of this work are two-fold: First, an offline design framework is proposed to detect the maximum unsuppression delay time and formulate dynamic alarm limits; second, an online algorithm for alarm monitoring of equipment start-ups is proposed on the basis of the designed dynamic alarm limits and the calculation of an exact unsuppression delay time. The effectiveness and practicality of the proposed method are demonstrated by an industrial case study.