Spaceborne large aperture membrane microstrip reflectarray antenna has the characteristics of high gain, lightweight and small storage volume, which will be used in future space missions. However, there are two main reasons restricting its application. Firstly, the traditional dimensional optimization method cannot effectively affect the distribution of prestress in the membrane reflector, so it needs to increase too much mass to achieve the goal of stiffness improvement; secondly, low stiffness makes the membrane reflector more sensitive to various uncertainties. In view of this, this paper proposes a method to affect the distribution of prestress by sticking irregular shaped additional layer, and proposes a non-probabilistic uncertain topology optimization method to design the shape of additional layer. The effectiveness of the proposed methods is verified by numerical examples. [ABSTRACT FROM AUTHOR]