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A space travelling wave tube (STWT) is an important microwave device that serves as the final-stage power amplifier in satellite systems and performs high-power signal conversion. The focus of this paper is the multi-objective problem of improving the electronic beam efficiency and suppressing nonlinear distortion for the slow-wave structure design of the STWT. We propose a design method based on multi-objective cat swarm optimization with gravitational search operator (GS-MOCSO) to improve the slow-wave structure. Electron beam efficiency and phase shift are used as the two objective functions, and 1-D CHRISTINE code is introduced to obtain the output value of the STWT. Finally, the best pitch distribution can be calculated by GS-MOCSO. An experiment is conducted based on GS-MOCSO, and the traditional multi-objective cat swarm optimization (MOCSO) is introduced for a baseline performance comparison. The experimental results demonstrate that the electronic beam efficiency on the best pitch distribution obtained by GS-MOCSO reaches 40.2%, which is 10.2% higher than the rated value of 30%. Moreover, it is higher than the value achieved by MOCSO, which reaches only 38.5%. Then, the phase shift is only 36.5°, which is a reduction of 23.5° compared to the value 60° under a constant pitch. Extensive investigations were also performed on the varying trends of beam efficiency and phase shift using input power scanning. The proposed method is highly suitable for the slow-wave structure design of STWT, and the GS-MOCSO algorithm is superior to the MOCSO algorithm for the multi-objective problem (MOP) of beam efficiency and phase shift. [ABSTRACT FROM AUTHOR]