A general study of the Seidel aberration of the lens systems made of left-handed media is presented according to the primary aberration theory. The Seidel aberration of the planar interface between air and left-handed medium was analyzed showing that its surface shape are more abundant when it is free from spherical aberration and it could be applied to real imaging systems. Based on the Seidel sum formulae of thin lens, three types of left-handed media thin lenses free from partial Seidel aberrations are designed with specific parameters. Finally, the Seidel aberration-free lens systems based on the use of left-handed media are presented. It is pointed out that left-handed media can be used to simplify the structure of lens system for the same or superior imaging performance.