Deep learning has achieved remarkable success in object recognition tasks through the availability of large scale datasets like ImageNet. However, deep learning systems suffer from catastrophic forgetting when learning incrementally without replaying old data. For real-world applications, robots also need to incrementally learn new objects. Further, since robots have limited human assistance available, they must learn from only a few examples. However, very few object recognition datasets and benchmarks exist to test incremental learning capability for robotic vision. Further, there is no dataset or benchmark specifically designed for incremental object learning from a few examples. To fill this gap, we present a new dataset termed F-SIOL-310 (Few-Shot Incremental Object Learning) which is specifically captured for testing few-shot incremental object learning capability for robotic vision. We also provide benchmarks and evaluations of 8 incremental learning algorithms on F-SIOL-310 for future comparisons. Our results demonstrate that the few-shot incremental object learning problem for robotic vision is far from being solved.