Existing LiDAR-inertial-visual odometry and mapping (LIV-SLAM) systems mainly utilize the LiDAR-inertial odometry (LIO) module for structure reconstruction and the visual-inertial odometry (VIO) module for color rendering. However, the accuracy of VIO is often compromised by photometric changes, weak textures and motion blur, unlike the more robust LIO. This paper introduces SR-LIVO, an advanced and novel LIV-SLAM system employing sweep reconstruction to align reconstructed sweeps with image timestamps. This allows the LIO module to accurately determine states at all imaging moments, enhancing pose accuracy and processing efficiency. Experimental results on two public datasets demonstrate that: 1) our SRLIVO outperforms existing state-of-the-art LIV-SLAM systems in both pose accuracy and time efficiency; 2) our LIO-based pose estimation prove more accurate than VIO-based ones in several mainstream LIV-SLAM systems (including ours). We have released our source code to contribute to the community development in this field.