We study the ground state solutions of the following quasilinear Kirchhoff type equation -( 1 + b integral(R3) vertical bar del u vertical bar(2) dx) Delta u + V (x) u - [Delta(u(2))]u = vertical bar u vertical bar(10)u + mu vertical bar u vertical bar(p-1)u, x is an element of R, where b >= 0 and mu is a positive parameter. Under some suitable conditions on V (x), we obtain the existence of ground stat...