In business process, similarity is important for comparing between business process models. The existing similarity methods, such as Graph-based Matching Method (GMA), Weighted Graph Edit Distance (WGED), Weighted Node Adjacent Relation Similarity (WNARS), Tree Declarative Pattern Edit Distance (TPED) and Cosine-Tree Declarative Pattern (Cosine-TDP) can distinguish between AND, OR, and XOR relationships. However, they have drawbacks in detecting same relationships with different event logs. This paper proposes a new similarity method based on weighted graph models called weighted graph-based parallel process model matching (WGPPM) for computing the behaviour of parallel activity relationships. The proposed method utilizes the frequency of activity relationships as the weight in the graph model to measure the similarity between processes containing parallel relationships. WGPPM is compared with GMA, WGED, WNARS, TPED, and Cosine-TDP. The result shows that WGPPM is able to compute similarity between same parallel relationship with different event logs.