Tendon-driven continuum robots are widely used in different engineering disciplines due to their simple structure and high flexibility. The typical structure of a tendon-driven continuum robot usually contains a series of identical compliant joints in its backbone to achieve large-deflection bending movements. However, with compliant joints of the same geometry, the real bending shape of the robot backbone is an arc with variable curvature, which results in uneven stress distribution along the robot backbone. In the long term, higher stresses in the compliant joints near the fixation base could lead to fatigue or fracture of the entire robot structure. To cope with this problem, we propose a fish-tail-inspired method in this letter to optimize the stress distribution along the serial compliant joints. Several optimization examples were presented to show the performance of the proposed method. Simulation and experimental results have demonstrated that the developed method can effectively reduce the stress differences in serial compliant joints during large-deflection bending movements.