In this paper, we propose a new airway segmentation algorithm from 3D chest CT volumes based on the volume of interest (VOI). The algorithm segments each bronchial branch by recognizing the airway regions from the trachea using the VOIs to segment each branch. A VOI is placed to envelop the branch currently being processed. Then a cavity enhancement filter is performed only inside the current VOI so that each branch is extracted. At the same time, we perform a leakage detection scheme to avoid any leakage regions inside the VOI. Next the gradient vector flow magnitude map and a tubular-likeness function are computed in each VOI. This assists the predictions of both the position and direction of the next child VOIs to detect the next child branches to continue the tracking algorithm. Finally, we unify all of the extracted airway regions to form a complete airway tree. We used a dataset that includes 50 standard-dose human chest CT volumes to evaluate our proposed algorithm. The average extraction rate was approximately 78.1% with a significantly decreased false positive rate compared to the previous method.