Head and neck (HN) gross tumor volume (GTV) auto-segmentation is challenging due to the morphological complexity and low image contrast of targets. Multi-modality images, including computed tomography (CT) and positron emission tomography (PET), are used in the routine clinic to assist radiation oncologists for accurate GTV delineation. However, the availability of PET imaging may not always be guaranteed. To develop a deep learning segmentation framework for automated GTV delineation of HN cancers using a combination of PET/CT images, while addressing the challenge of missing PET data. Two datasets were included for this study: Dataset I: 524 (training) and 359 (testing) oropharyngeal cancer patients from different institutions with their PET/CT pairs provided by the HECKTOR Challenge; Dataset II: 90 HN patients(testing) from a local institution with their planning CT, PET/CT pairs. To handle potentially missing PET images, a model training strategy named the "Blank Channel" method was implemented. To simulate the absence of a PET image, a blank array with the same dimensions as the CT image was generated to meet the dual-channel input requirement of the deep learning model. During the model training process, the model was randomly presented with either a real PET/CT pair or a blank/CT pair. This allowed the model to learn the relationship between the CT image and the corresponding GTV delineation based on available modalities. As a result, our model had the ability to handle flexible inputs during prediction, making it suitable for cases where PET images are missing. To evaluate the performance of our proposed model, we trained it using training patients from Dataset I and tested it with Dataset II. We compared our model (Model 1) with two other models which were trained for specific modality segmentations: Model 2 trained with only CT images, and Model 3 trained with real PET/CT pairs. The performance of the models was evaluated using quantitative metrics, including Dice similarity coefficient (DSC), mean surface distance (MSD), and 95% Hausdorff Distance (HD95). In addition, we evaluated our Model 1 and Model 3 using the 359 test cases in Dataset I. Our proposed model(Model 1) achieved promising results for GTV auto-segmentation using PET/CT images, with the flexibility of missing PET images. Specifically, when assessed with only CT images in Dataset II, Model 1 achieved DSC of 0.56±0.16, MSD of 3.4±2.1mm, and HD95 of 13.9±7.6mm. When the PET images were included, the performance of our model was improved to DSC of 0.62±0.14, MSD of 2.8±1.7mm, and HD95 of 10.5±6.5mm. These results are comparable to those achieved by Model 2 and Model 3, illustrating Model 1's effectiveness in utilizing flexible input modalities. Further analysis using the test dataset from Dataset I showed that Model 1 achieved an average DSC of 0.77, surpassing the overall average DSC of 0.72 among all participants in the HECKTOR Challenge. We successfully refined a multi-modal segmentation tool for accurate GTV delineation for HN cancer. Our method addressed the issue of missing PET images by allowing flexible data input, thereby providing a practical solution for clinical settings where access to PET imaging may be limited.