In this work, we present a visual-inertial-pressure (VIP) fusion method for underwater robot localization. Specifically, this letter focuses on the tightly-coupled fusion of pressure measurements into a visual inertial odometry (VIO) based on sliding window optimization. Previous works used to associate partial pressure measurements with the nearest keyframes, which not only fail to utilize all the pressure measurement information but also introduce measurement errors that only lead to sub-optimal solutions. Inspired by the current tightly-coupled visual-inertial-GPS and visual-inertial-UWB fusion methods, this letter uses IMU preintegration algorithm to derive the pressure factors. Furthermore, we propose a backward IMU preintegration method and the pressure factors are derived using forward or backward IMU preintegration based on the time-offset between the pressure measurements and the adjacent keyframes. Quantitative and qualitative analyses through simulation and real-world datasets experiments demonstrate the effectiveness of the method with negligible time cost.