Free-edge effect is known to play an important role in the failure of triaxially braided composites, especially under transverse tension loading conditions. However, there is little understanding available regarding the free-edge effect on the elastic property of the material. The emphasis of the present study is to examine the impact of the free-edge effect on the effective elastic response of a single-layer triaxially braided composite. Transverse tension straight-sided coupon specimens with various widths are tested and analyzed. The experimental results demonstrate an obvious increase in the tangent modulus and failure strength as the specimen width increases. The surface out-of-plane displacement contours present a continuous out-of-plane warping behavior distributed periodically along the free edges in an antisymmetric way. A meso-scale finite element model is utilized to study the coupon specimens; it is found to correlate well with the experimental data in predicting elastic properties and out-of-plane warping behavior. The results indicate that free-edge effect is an inherent factor of the antisymmetric braided architecture of bias fiber bundles. By conducting a dimensional analysis, the relationships between effective moduli and specimen width are quantified using Weibull equations; this method could potentially be used to predict the material properties of large structural components using small-scale test data.