A non-parametric low-resolution face recognition model for resource-constrained environments with limited networking and computing is proposed in this work. Such environments often demand a small model capable of being effectively trained on a small number of labeled data samples, with low training complexity, and low-resolution input images. To address these challenges, we adopt an emerging explainable machine learning methodology called successive subspace learning (SSL).SSL offers an explainable non-parametric model that flexibly trades the model size for verification performance. Its training complexity is significantly lower since its model is trained in a one-pass feedforward manner without backpropagation. Furthermore, active learning can be conveniently incorporated to reduce the labeling cost. The effectiveness of the proposed model is demonstrated by experiments on the LFW and the CMU Multi-PIE datasets.