Motion planning is the basis for the motion control. However, motion planning for a cannula flexible needle insertion in the soft tissue is a great challenge. On the one hand, the kinematics of the needle is a nonholonomic motion, and on the other hand, the needle has to steer clear of the anatomical obstacles and sensitive organs to reach the target precisely. By analyzing the deficiency of existing motion planning algorithms, a motion planning algorithm for the cannula flexible needle is proposed based on an improved RapidlyExploring Random Trees (RRT). The GreedyHeuristic strategy is proposed, which is combined with the ReachabilityGuided strategy to improve the conventional RRT. Linear segment is introduced into the planning, and the combination path of the linear and curvilinear segments is adopted. Insertion orientations are taken into account at the same time. Simulations are performed in 2D and 3D environments with obstacles based on the kinematic model of the needle. Results show that the proposed algorithm yields superior results compared with the commonly used algorithm in terms of computational speed, convergence, form of path and robustness of searching ability. These superiorities potentially provide the basis for the upcoming realtime motion planning. At last, the experiment for the planned path is carried, and experimental results show that experimental paths agree with the planned ones very well, which not only proves the validity of the proposed path planning algorithm but also proves the feasibility of the planned path.