In existing continuum robots, not every segment within a section is controlled, limiting the full utilization of their flexibility and making navigation through narrow and continuously curved spaces challenging. This paper introduces a single-section controllable continuum robot where each segment can be independently controlled via driving wires. Firstly, we designe the structure and connection method of the continuum robot segments. Secondly, we establish the kinematic model of the single-section controllable continuum robot, enabling independent control of each segment through the driving wires. Finally, we compares and tests the fitting accuracy of different configurations of continuum robots with controllable parts containing 1, 3, 5, and 7 segments in one section, regarding their ability to fit the same curve. The single-section controllable continuum robot can independently control the position of each joint within the continuum, demonstrating superior curve fitting capability and enabling navigation through narrow, continuously curved spaces.