Most of the available creep prediction models proposed by the different national building codes are valid only for concretes having compressive strengths not greater than 800kgf/cm2 (80MPa). A rheological viscoelastic model is proposed for predicting the creep of normal- and high-strength concretes from their basic constituents, that are cement paste and aggregate. A parametric study is carried out to compare the creep functions calculated using CEB-FIP Model Code 1990 and ACI Committee 209 with those calculated using the proposed model as well as with the available experimental data. The comparison indicated that the proposed model can predict the creep of both normal- and high-strength concretes.