Recent trends in Large Vision Language Models (LVLMs) research have been increasingly focusing on advancing beyond general image understanding towards more nuanced, object-level referential comprehension. In this paper, we present and delve into the self-consistency capability of LVLMs, a crucial aspect that reflects the models' ability to both generate informative captions for specific objects and subsequently utilize these captions to accurately re-identify the objects in a closed-loop process. This capability significantly mirrors the precision and reliability of fine-grained visual-language understanding.Our findings reveal that the self-consistency level of existing LVLMs falls short of expectations, posing limitations on their practical applicability and potential. To address this gap, we introduce a novel fine-tuning paradigm named \textbf{Self-Consistency Tuning (SC-Tune)}. It features the synergistic learning of a cyclic describer-locator system. This paradigm is not only data-efficient but also exhibits generalizability across multiple LVLMs. Through extensive experiments, we demonstrate that SC-Tune significantly elevates performance across a spectrum of object-level vision-language benchmarks and maintains competitive or improved performance on image-level vision-language benchmarks. Both our model and code will be publicly available.