Virtual Bronchoscopy (VB) permits the preplanning of operations concerning the airways and provides the necessary guidance to reach the pulmonary lesions. Fundamental for a good VB is the reconstruction of a 3D model of the airways from the CT images. Airway segmentation algorithms usually return the biggest detected volume connected to the trachea (the root tree), but many of them also reconstruct during the segmentation process, small parts not connected to the root tree. To overcome this problem this paper proposes a method, based on path planning techniques, that is able to connect the small isolated pieces of bronchi to the terminal points of the root airway tree, taking into account the growing direction of the branches and the gray values of the CT images. As a result, a more complete 3D model of the airways is obtained.