The different importance of the activities in the business process in real world is not taken into account by the existing cost functions, so that in the alignment process of model and log, alignment cost may deviates from perceived cost significantly. To solve this problem, a concept of important synchronization cost function was proposed based on the typical flow characteristic of the behaviors in business processes, and an alignment method that can improve efficiency was proposed under this function. Firstly, the important synchronization cost function was defined based on the concept of perceived cost. Then, the important matching sub-sequence to segment the process model and the log trace was determined according to the log trace and the typical flow characteristic of the behaviors in the process model. Finally, based on the important synchronization cost function, the segmented sub-process and the corresponding log trace subsequence were aligned, and the segmented alignment results were combined to obtain the final alignment result. The experiments were carried out to verify the proposed method from the perspectives of accuracy and efficiency. In terms of accuracy, compared with the existing standard cost function and maximum synchronous cost function, the proposed cost function improved the alignment accuracy by up to 17.44 percentage points, and when the event log contained mixed noise, the proposed cost function had the highest average alignment accuracy of 88.67%. The efficiency of alignment was verified by comparing the time consumed by alignment. The average time of the existing two functions were 1.58 s and 2.21 s respectively, while that of the proposed method was 0.63 s, which was improved by 150.79% and 250.79% respectively. Experimental results show that the proposed method can satisfy the accuracy demand and improve the efficiency of alignment at the same time.