In this paper, we proposes a man-machine interface design for fault diagnosis system with inter-node search method in a Petri net model. First, complicated fault cases are modeled as the Petri net graph expressions. Next, to find out causes of the faults on which we focus, a Petri net model is analyzed using the backward reasoning of transition-invariance in the Petri net. In this step, the inter-node search method algorithm is applied to the Petri net model for reducing the range of sources in faults. Finally, the proposed method is applied to a fault diagnosis of a refrigeration system to confirm the validity of the proposed method.