Rapidly-exploring Random Tree star （RRT^*） is widely used in the robot path planning field owing to its asymptotic optimality and probabilistic completeness. However， RRT^* and its improved algorithms still suffer from several limitations such as poor initial path quality， slow path convergence， and low search efficiency. In response to these challenges， an adaptive extended RRT^* algorithm based on node-to-obstacle distance， namely AE-RRT^*， was proposed. To improve the search efficiency， a dynamic goal-biased sampling strategy and a dynamic step size strategy based on the node-to-obstacle distance were adopted. Furthermore， to improve the path quality， a more accurate parent node choice method MA-ChooseParent was proposed， which broadened the set of potential parent nodes. In addition， to speed up path convergence， an adaptive Gaussian sampling method and a global Gaussian sampling method AG-Gaussian Sample based on the node-to-obstacle distance were adopted. Through simulation in Matlab， AE-RRT^* was compared with RRT^*， Quick-RRT^*， Bi-RRT^*， Informed-RRT^*， and Smart-RRT^*. Experimental results demonstrate that compared to RRT^*， AE-RRT^* achieves reductions of 63.78%， 6.55%， and 71.93%， respectively， in the time taken to find the initial path， the length of the initial path， and the time to converge to a global sub-optimal path in 2D environments. In 3D environments， AE-RRT^* achieves reductions of 59.44%， 18.26%， and 79.58%， respectively， in the three indicators.