Scale effect of compressive strength of ordinary concrete and high strength concrete were investigated through compression experiments on ordinary concrete and high strength concrete specimens with the strength grade of C20, C40 and C60, and the specimen side length of 100, 150, 200mm. The relationship between the strength grade and scale effect was established. Then, the critical size and critical strength of ordinary concrete and high strength concrete were obtained. Furthermore, the computational equations of scale effect were proposed. Finally, good agreements have been found between tested data and the computational equations. The test and analysis results show that the scale effect exists in the cubic compressive strength of the ordinary concrete and high strength concrete. With an increase in the strength grade, the scale effect is significantly enhanced. The scale effect of concrete with strength grade C20 is 55% of the concrete with strength grade C60.