In CPU-GPU hybrid systems, the QR factorization in MAGMA re- sults in CPU idle due to the xed block size. To improve the computa- tional e ciency of MAGMA QR factorization, we propose a dynamic block size auto-tuning scheme on CPU-GPU hybrid systems. Our approach is a data-driven approach. First we model the CPU and GPU costs in MAGMA QR factorization via two independent regression models based on collecting training data. Next, according to these tting models, we propose a block size optimization scheme to tune the block size adaptively and therefore to minimize a cost objective function. The cost objective function is designed to balance the workloads between CPU and GPU based on the performance models. Several numerical results demonstrate the performance gains due to the novel QR factorization algorithm.