Active reconstruction technique enables robots to autonomously collect scene data for full coverage, relieving users from tedious and time-consuming data capturing process. However, designed based on unsuitable scene representations, existing methods show unrealistic reconstruction results or the inability of online quality evaluation. Due to the recent advancements in explicit radiance field technology, online active high-fidelity reconstruction has become achievable. In this paper, we propose GS-Planner, a planning framework for active high-fidelity reconstruction using 3D Gaussian Splatting. With improvement on 3DGS to recognize unobserved regions, we evaluate the reconstruction quality and completeness of 3DGS map online to guide the robot. Then we design a sampling-based active reconstruction strategy to explore the unobserved areas and improve the reconstruction geometric and textural quality. To establish a complete robot active reconstruction system, we choose quadrotor as the robotic platform for its high agility. Then we devise a safety constraint with 3DGS to generate executable trajectories for quadrotor navigation in the 3DGS map. To validate the effectiveness of our method, we conduct extensive experiments and ablation studies in highly realistic simulation scenes.