The correlation between shape and size of linear chains on the simple cubic lattice is investigated using a dynamic Monte Carlo technique. A positive correlation between the asphericity parameter A and the square of the end-to-end distance R2, as well as that between A and the square of the radius of gyration S2, is found for both RW and SAW chains, indicating that a chain conformation of small size is usually more spherical than one of large size. The result can explain why the shape of the SAW chain deviate much more from a sphere than that of the RW chain, and can also explain the similar dependence of size and shape on chain stiffness and on the distance of the first bead of a chain from an infinitely large flat surface.