Abstract: We study the existence of solutions for fractional Hamiltonian systems. We consider the potential function W(t,u) with parameters to satisfy the new superlinear and sublinear combination conditions W(t,u) = W_1(t,u) + \mu W_2(t,u), \mu > 0. When \left| u \right| \to \infty , W_1(t,u) satisfies the more general superlinear growth conditions, instead of the Ambrosetti-Rabinowitz condition; W_2(t,u) satisfies more general sublinear growth conditions. In this part, we need to establish a new compact embedding theorem to verify the compactness of the sequence. Using the critical point theory, the existence results of two solutions of the above system are obtained.