Abstract: In the space-borne gravitational wave detection missions, test mass capture is critical for the spacecraft to enter the super-stable flight state. This process is characterized by large initial errors, large system uncertainties and strong execution constraints. This paper presents an improved high precision elastic tube model predictive control of test mass capture. A control structure based on rolling optimization and elastic tube technology is proposed to improve the capture success rate and effectively compensate the satellite coupling interference on test mass. The tiny tolerance active set method is proposed to improve the accuracy of online calculation and ensure the high control accuracy of test mass. Meanwhile, this paper proposes an offline correction method for the minimum robust positive invariant set based on feature engineering. It reduces the vertices of the minimum robust positive invariant set based on the Minkowski summation and reduces the online computational complexity. The proposed method is verified by simulations on the space-based double test masses full-freedom simulation platform. The results show that the control performance satisfies the test mass capture accuracy requirement. The controller is robust and the rate of convergence is improved effectively. The effects of platform motion interference and measurement noise are suppressed.