Development rule of compressive strength and elastic modulus of different strength grades limestone aggregate concrete was investigated and compared with sandstone aggregate concrete. The relationship among compressive strength, elastic modulus and age of limestone aggregate concrete was established through numerical simulation. The results show that the elastic modulus of different strength grades limestone aggregate concrete grows more quickly than its compressive strength and is higher than that of sandstone aggregate concrete. The relationship between the elastic modulus and the square root of compressive strength of concrete with different lithological aggregates and strength grades is linear. With the increase of strength grade of concrete, the limestone aggregate concretes elastic modulus growth slows down and is contrary to the sandstone aggregate concrete.