We propose a novel framework for filtering image-text data by leveraging fine-tuned Multimodal Language Models (MLMs). Our approach outperforms predominant filtering methods (e.g., CLIPScore) via integrating the recent advances in MLMs. We design four distinct yet complementary metrics to holistically measure the quality of image-text data. A new pipeline is established to construct high-quality instruction data for fine-tuning MLMs as data filters. Comparing with CLIPScore, our MLM filters produce more precise and comprehensive scores that directly improve the quality of filtered data and boost the performance of pre-trained models. We achieve significant improvements over CLIPScore on popular foundation models (i.e., CLIP and BLIP2) and various downstream tasks. Our MLM filter can generalize to different models and tasks, and be used as a drop-in replacement for CLIPScore. An additional ablation study is provided to verify our design choices for the MLM filter.