In this paper, we will consider certain amalgamated free product structure in crossed product algebras. Let M be a von Neumann algebra acting on a Hilbert space Hand G, a group and let : G AutM be an action of G on M, where AutM is the group of all automorphisms on M. Then the crossed product G of M and G with respect to is a von Neumann algebra acting on , generated by M and , where is the unitary representation of g on . We show that . We compute moments and cumulants of operators in . By doing that, we can verify that there is a close relation between Group Freeness and Amalgamated Freeness under the crossed product. As an application, we can show that if is the free group with N-generators, then the crossed product algebra satisfies that , whenerver .