This paper considers active SLAM problem for 3D deformable environments where the trajectory of the robot is planned to optimize the SLAM results. A planning strategy combining an efficient global planner with an accurate local planner is proposed to solve the problem. Simulation results under different scenarios have shown that the proposed active SLAM algorithm provides a good balance between accuracy and efficiency as compared to the local planner and the global planner. The MATLAB code of this first active SLAM algorithm for 3D deformable environments is made publicly available⁴.