The continuum robot is a new type of bionic robot which is widely used in the medical field. However, the current structure of the continuum robot limits its application in the field of minimally invasive surgery. In this paper, a bio-inspired compound continuum robot (CCR) combining the concentric tube continuum robot (CTR) and the notched continuum robot is proposed to design a high-dexterity minimally invasive surgical instrument. Then, a kinematic model, considering the stability of the CTR part, was established. The unstable operation of the CCR is avoided. The simulation of the workspace shows that the introduction of the notched continuum robot expands the workspace of CTR. The dexterity indexes of the robots are proposed. The simulation shows that the dexterity of the CCR is 1.472 times that of the CTR. At last, the length distribution of the CCR is optimized based on the dexterity index by using a fruit fly optimization algorithm. The simulations show that the optimized CCR is more dexterous than before. The dexterity of the CCR is increased by 1.069 times. This paper is critical for the development of high-dexterity minimally invasive surgical instruments such as those for the brain, blood vessels, heart and lungs.