This study presents a new perspective for autonomous mobile robots path searching by proposing a biasing direction towards causal entropy maximisation during random tree generation. Maximum entropy-biased rapidly-exploring random tree (ME-RRT) is proposed where the searching direction is computed from random path sampling and path integral approximation, and the direction is incorporated into the existing rapidly-exploring random tree (RRT) planner. Properties of ME-RRT including degenerating conditions and additional time complexity are also discussed. The performance of the proposed approach is studied, and the results are compared with conventional RRT/RRT* and goal-biased approach in 2D/3D scenarios. Simulations show that trees are generated efficiently with fewer iteration numbers, and the success rate within limited iterations has been greatly improved in complex environments.