In this letter, we propose RI-LIO, a new reflectivity image assisted tightly-coupled LiDAR-inertial odometry (LIO) framework that introduces additional reflectivity texture information to efficiently reduce the drift of geometric-only methods. To achieve this, we construct an iterated extended Kalman filter framework by blending the point-to-plane geometric measurement and the reflectivity image measurement. Specifically, the geometric measurement is defined as the distance from the raw point of a new scan to its nearest neighbor plane in the global incremental kd-tree map. The searched nearest neighbor point is used to render a sparse reflectivity image after LiDAR motion distortion information is given by its corresponding raw point. Then, the reflectivity measurement is built to align the sparse reflectivity image with the dense reflectivity image of the current scan by minimizing the photometric errors directly. In addition, based on the mechanism of high-resolution LiDAR, a corrected spherical projection model is proposed to project spatial points into the image frame. Finally, extensive experiments are conducted in structured, unstructured and challenging open field scenarios. The results demonstrate that the proposed method outperforms existing geometric-only methods in terms of robustness and accuracy, especially in the rotation direction.