Recent text-to-image (T2I) models have benefited from large-scale and high-quality data, demonstrating impressive performance. However, these T2I models still struggle to produce images that are aesthetically pleasing, geometrically accurate, faithful to text, and of good low-level quality. We present VersaT2I, a versatile training framework that can boost the performance with multiple rewards of any T2I model. We decompose the quality of the image into several aspects such as aesthetics, text-image alignment, geometry, low-level quality, etc. Then, for every quality aspect, we select high-quality images in this aspect generated by the model as the training set to finetune the T2I model using the Low-Rank Adaptation (LoRA). Furthermore, we introduce a gating function to combine multiple quality aspects, which can avoid conflicts between different quality aspects. Our method is easy to extend and does not require any manual annotation, reinforcement learning, or model architecture changes. Extensive experiments demonstrate that VersaT2I outperforms the baseline methods across various quality criteria.