Elastic gridshells are lightweight structures using the elastic bending of slender components to efficiently construct large-span freeform geometries. Due to outstanding bending capacity, as well as the ability to be made into long profiles, FRP has been increasingly used in elastic gridshells, making the structure an active field of interest and application. This paper introduces the design and construction process of a modular segment-assembling GFRP elastic weaving gridshell, the Infinity Pavilion. The pavilion consists of self-balancing rigid units that are connected by specially designed standard circular flanges with bolted joints, and can be prefabricated and flexibly combined on site. Double-layer gridshell is used to reduce the cross-sectional size of the rods while ensuring the overall stiffness of the structure, making construction easier for manual operation. An optimized kagome mesh is generated by semi-automatic methods to improve structural efficiency and standardize rod components. As a result, the 15 m * 9 m * 7 m structure can be constructed by GFRP rods with a diameter of 11mm and an overall weight of 695 kg, and the material usage is 5.15 kg/m2 in average, showing the potential in realizing portable and variable structures with special geometry and large span.