This work focuses on the potential of vision large language models (VLLMs) in visual reasoning. Different from prior studies, we shift our focus from evaluating standard performance to introducing a comprehensive safety evaluation suite Unicorn, covering out-of-distribution (OOD) generalization and adversarial robustness. For the OOD evaluation, we present two novel visual question-answering (VQA) datasets, each with one variant, designed to test model performance under challenging conditions. In exploring adversarial robustness, we propose a straightforward attack strategy for misleading VLLMs to produce visual-unrelated responses. Moreover, we assess the efficacy of two jailbreaking strategies, targeting either the vision or language input of VLLMs. Our evaluation of 22 diverse models, ranging from open-source VLLMs to GPT-4V and Gemini Pro, yields interesting observations: 1) Current VLLMs struggle with OOD texts but not images, unless the visual information is limited; and 2) These VLLMs can be easily misled by deceiving vision encoders only, and their vision-language training often compromise safety protocols. We release this safety evaluation suite at https://github.com/UCSC-VLAA/vllm-safety-benchmark.