Gravitational waves are a significant prediction of Einstein's theory of general relativity and have important implications for human understanding of the origin of the universe and the structure of space–time. The libration point configuration is one of the configuration schemes for space gravitational wave detection. It consists of an interferometric measurement constellation composed of a spacecraft located near the Sun-Earth L2 libration point and two spacecraft moving in the Earth-leading and Earth-trailing orbits, respectively. This libration configuration has a long interferometric baseline, enabling it to detect low-frequency gravitational waves. Configuration stability is a crucial constraint in the design of space gravitational wave detection configurations and has a significant impact on the accuracy of measurements. This paper focuses on the study of libration point configuration schemes for space gravitational wave detection. First, the sensitivity of design parameters to configuration stability is analyzed. The phase angle of the Earth-leading/Earth-trailing orbit is found to be the most important factor. Then, using the analytical model of the Earth phase bias orbit, a two-step method is proposed to optimize the libration configuration. In the first step, the Earth's leading and trailing orbits are optimized to minimize the variation of the phase angles. Taking these orbits as initial guesses, in the second step, the stability index is used to find the optimal orbital parameters for a given libration orbit. Based on the proposed method, this paper further analyzes the impact of different amplitude orbits on the stability index and establishes the range of parameters for the libration orbit. The optimized scheme exhibits a maximum reduction of 50% in the stability criterion boundaries compared to the LAGRANGE scheme. The research findings could offer theoretical support for the design and implementation of future gravitational wave detection missions utilizing libration point configurations.