A number of structural collapses are initiated from losing stability locally. The monitoring and detection of instability is rarely studied in both research communities of structural health monitoring and structural stability. In order to capture member buckling at an early stage to prevent a local instability from propagating into an overall structural failure, in this study, an approach to detect one type of instability (member overall buckling) is proposed for civil large-scale space grid structures. The foundation of this approach lies in: once a member buckles, a large bending stress due to buckling is developed and dominates the total normal stress of the member. Since the bending stress varies along a member, the total normal stress varies along the member, so does the total normal strain on the surface of the member. Therefore, by identifying the deviation in normal strain at two different cross sections of a member, overall buckling of the member can be detected. This study will justify that strain gauges can pick up all the bending stress induced by buckling as long as they are deployed before buckling. Numerical simulations have been conducted on large-scale space grid structures with different types of connections between members and loading situations. The obtained results have shown that once a member buckles, the strains measured at two different cross sections on the member deviate from each other significantly, verifying the efficacy of the proposed approach.