Abstract: The characteristic longitudinal arrangement of fibers in pultruded glass fiber reinforced polymer (GFRP) circular tubes makes them suitable for space truss structures where the members are primarily subjected to axial forces. To establish a member computational model for direct second-order nonlinear analysis of assembled GFRP space truss structures, this paper focuses on GFRP truss members with bolt-ball joints. The whole process of axial compression bearing responses and failure modes were first obtained through axial compression tests, and the refined finite element model of solid-shell elements was used to further reveal that the bearing nonlinearity arises from the yielding of bolt-ball joints, the overall instability of GFRP tubes, and the splitting failure of GFRP tubes. On this basis, multi-segment equal-length beam elements were employed to simulate the initial bending of the members, and multiple sets of nonlinear spring elements were utilized to represent the bearing responses of the primary components. Consequently, a direct second-order nonlinear efficient analytical model of GFRP truss members with bolt-ball joints was established, which comprehensively considered all nonlinear factors. The applications in GFRP single members and single space truss structures showed that the efficient analysis model can accurately predict the ultimate bearing capacity and final failure displacement of structures, with relative errors of less than 3% for both quantities, and can greatly reduce the computational resource consumption for the computational analysis of large-scale assembled FRP space truss structures.