We prove the existence of a homoclinic orbit for Lagrangian system (LS) where the Lagrallgian L(t,x,y)=1/2 \sum a_ij(x)y_iy_j-V(t,x). A similar argument to Rabinowitz[5] is used, where a_ij (x) is an identity matrix. Now the differential equation is quasilinear and more estimates are needed to get the uniform bound for the second derivative of periodic sequence {x_k(t)} with period 2kT.