Since developing a new multimodal LLM (MLLM) by pre-training on tremendous image-text pairs from scratch can be exceedingly resource-consuming, connecting an existing LLM with a comparatively lightweight visual prompt generator (VPG) becomes a feasible paradigm. However, further tuning the VPG component of the MLLM still incurs significant computational costs, such as thousands of GPU hours and millions of training data points. An alternative solution is transferring an existing VPG from one MLLM to the target MLLM. In this work, we investigate VPG transferability across LLMs for the first time, aiming to reduce the cost of VPG training. Specifically, we explore VPG transfer across different LLM sizes (e.g., small-to-large) and types. We identify key factors to maximize transfer efficiency, based on which we develop a simple yet highly effective two-stage transfer framework, called VPGTrans. Notably, it enables VPG transfer from BLIP-2 OPT 2.7B to BLIP-2 OPT 6.7B with less than 10% of the GPU hours using only 10.7% of the training data compared to training a VPG for OPT 6.7B from scratch. Furthermore, we provide a series of intriguing findings and discuss potential explanations behind them. Finally, we showcase the practical value of our VPGTrans approach, by customizing two novel MLLMs, including VL-LLaMA and VL-Vicuna, with recently released LLaMA and Vicuna LLMs.