We developed a kernelled support tensor machine (KSTM)-based model with tumor tensors derived from pre-treatment PET and CT imaging as input to predict distant failure in early stage non-small cell lung cancer (NSCLC) treated with stereotactic body radiation therapy (SBRT). The patient cohort included 110 early stage NSCLC patients treated with SBRT, 25 of whom experienced failure at distant sites. Three-dimensional tumor tensors were constructed and used as input for the KSTM-based classifier. A KSTM iterative algorithm with a convergent proof was developed to train the weight vectors for every mode of the tensor for the classifier. In contrast to conventional radiomics approaches that rely on handcrafted imaging features, the KSTM-based classifier uses 3D imaging as input, taking full advantage of the imaging information. The KSTM-based classifier preserves the intrinsic 3D geometry structure of the medical images and the correlation in the original images and trains the classification hyper-plane in an adaptive feature tensor space. The KSTM-based predictive algorithm was compared with three conventional machine learning models and three radiomics approaches. For PET and CT, the KSTM-based predictive method achieved the highest prediction results among the seven methods investigated in this study based on 10-fold cross validation and independent testing.