To solve the difficult problem of non-interference movement path planning of electrodes of complex cavity-type parts in electric discharge machining (EDM), an electrode movement trajectory search algorithm is proposed. The algorithm is based on the non-uniform rational B-splines (NURBS) parametric curve surface method, which is used to fit the blade profile and establish the accurate mathematical model of the blade. The method of calculating the runner centerline is given, and the trajectory search algorithm is proposed based on the expression of the runner centerline. A special computer aided manufacturing (CAM) system for multi-axis linkage EDM machining of complex cavity parts was developed using the proposed algorithm. The electrode movement path planning and non-interference machining process simulation of 4-axis, 5-axis and 6-axis complex cavity-type parts are carried out, and the machining experiment of the integral turbine disc with blade crown is conducted. The results show that the machining accuracy of the blade shape is less than 0.03 mm, and the total time is 249.3 h, which satisfies the index requirements of the closed integral blisk parts. Experiments show that the algorithm can quickly search for the motion trajectory of non-interference electrode, effectively avoid electrode interference, thereby improving the efficiency of trajectory search, and strong adaptability to working conditions, which can be used to search for trajectories of electrode motion of complex cavity-type parts such as impellers and blisks under various working conditions of 4–6 axes.