This study presents a new approach for determination of tensile strength ft and fracture toughness KIC of concrete using wedge-splitting (WS) specimens as neither property can be easily measured because of the heterogeneous material structures. The Boundary Effect Model (BEM) was extended to WS geometry and relevant equations were derived so that more concrete properties can be determined by the load and displacement measurements. The new model considers the influence of coarse aggregate structures on concrete fracture by linking the fictitious crack growth Δafic at peak load Pmax to the maximum aggregate size dmax. The random aggregate distribution and inevitable variations in Δafic and Pmax are considered by a discrete number β. WS results of concrete specimens with dmax from 10 mm to 25 mm and specimen size W from 150 mm to 1200 mm reported in literature are analyzed for a range of β from around 0.2 to 2.0. It is found that on average β ≈ 1 is a good approximation for common WS specimens with W/dmax < 20. Then reliable ft and KIC, which is the asymptotic limit for a large structure with a long crack, can be obtained, regardless whether WS specimens are geometrically similar, or have the same size but different notch lengths. Finally, it is concluded that quasi-brittle fracture of concrete is fully predicted if both KIC and ft are known.