The recently-developed boundary effect concept and the associated asymptotic model are used to analyze size-dependent fracture of concrete specimens. It is shown that the dependence of concrete fracture on specimen size, crack and/or ligament length is due to the same mechanism, i.e. the interactions between the crack tip fracture process zone and specimen's boundaries. By introducing an equivalent crack length ae, dimension dependent fracture becomes equivalent to fracture of a large plate with a small edge crack, and therefore, follows the same relationship of the "net" nominal strength σn versus ae. As a result, the size dependent fracture can be predicted using the data measured on different types of specimens. To demonstrate the flexibility and effectiveness of the asymptotic boundary effect model, previously published results of three test series are analyzed. Excellent agreement has been found. Implications of the successful prediction are discussed.