The problem of the number of limit cycles for three classes of Liénard systems, that is, (m, n)=(9,7), (m, n)=(8,7) and (m, n)=(7,8) , are studied in the neighbourhood of the origin. The first ten, nine and nine singular point values for the corresponding accompany complex systems are calculated by using the computer algebra system, Mathematica, and the method of singular point values. Then, three kinds of Liénard system can generate at least ten, nine and nine limit cycles at the sufficiently small neighborhood of the origin respectively. And the exitence of limit cycle is proved by applying the Jacobian determinant method. It is the first time for giving the lower bound estimates for such systems, that is, H^(9,7)≥10,H^(8,7)≥9,H^(7,8)≥9.