This paper proposes a reconstruction method of the as-built model of plant piping, where the port point of the fitting is used as the secondary reference point, which represents a connection point between the fitting and its connected pipeline. The connection point between a fitting and a pipeline is a critical point of reference in the as-built model. In this study, a fitting model is registered to the point clouds first by using the state-of-the-art technique, which is based on an iterative closest point (ICP) algorithm and also considers the alignment of the port direction with the connected pipelines. Then, the port points of the registered fitting are considered as connection points, and the nozzle points of the connected pipelines are adjusted along its axis based on the information. After the registration process, which uses the detailed shape of fitting and the directions of adjacent pipelines at the same time, the port point on the registered fitting becomes a better estimate of the connection point compared with the nozzle point of a pipeline detected.