Due to the space constraints and obstacles, the traditional industrial manipulator is too difficult to achieve some tasks, such as the gluing for the wing bulkhead of the aircraft and the maintenance for cooling pipes of the nuclear power plant, etc. Continuum manipulator, inspired by the trunk and the tentacle, proves to be very effective for above-mentioned tasks. A novel octopus-like biomimetic robots, is proposed in this paper, which is consisting of continuum joints and discrete joints, and provide a host of benefits, such as the large space of movement, the high flexibility and the heavy load. A novel analytical approach for solving kinematics of the octopus-like arm manipulator with mixed joints is presented in this paper. Based on the bionic mechanism of the continuum manipulator constructed from mixed joints, the robot configuration is established. In this paper, we present a detailed formulation and explanation of a novel kinematic model for the continuum robots with mixed joints. The modeling method based on the Denavit–Hartenberg parameters(also called DH parameters) is used to depict the motion of robot. The robot is comprised of the continuum joint and the rotated joint, so the kinematic model of continuum joint is crucial for constructing that of the whole robot. The continuum joint is equivalent to a section of elastic body, whose D-H parametors can be obtain from the constant-curvature method. Then the forward kinematics of the whole robot can be builded in a D-H frame. Research results will create a new modeling method for the octopus-like continuum manipulators with mixed joints, which can give a new approach for the design on the biomimetic manipulators operating in the unstructured envirement.