Due to a large number of redundant degrees of freedom (DOFs), the hyper-redundant manipulator shows outstanding dexterity and adaptability in avoiding the obstacles in confined space. In this paper, a hybrid obstacle-avoidance method of spatial hyper-redundant manipulators is proposed, with both efficiency and accuracy considered. The space around an obstacle is classified into safe, warning, and dangerous zones. A two-level protection strategy is then addressed to handle the obstacle-avoidance problem from qualitative (i.e., pseudo-distance based on super-quadric function) and quantitative (i.e., Euclidean distance based on practical geometry function) perspectives, respectively. The only condition for switching between the two-level protections is the value of pseudo-distance. Then, a modified modal method, which is a trajectory planning method, is presented to plan the collision-free trajectory of the manipulator by maximizing the minimum pseudo-distance or Euclidean distance in different zones. Some parameters, including the arm-angle parameters and the equivalent link length parameters, are defined to represent the manipulator configuration. They are adjusted to avoid the obstacle, singularity, and joint limit. The simulations of 12-DOF manipulator and an experiment of 18-DOF manipulator verify the proposed methods.