The Wigner function's behavior of accelerated and non-accelerated Greenberger Horne Zeilinger (GHZ) state is discussed. For the non-accelerated GHZ state, the minimum/maximum peaks of the Wigner function depends on the distribution's angles, where they are displayed regularly at fixed values of the distribution's angles. We show that, for the accelerated GHZ state, the minimum bounds increases as the acceleration increases. The increasing rate depends on the number of accelerated qubits. Due to the positivity/ negativity behavior of the Wigner function, one can use it as an indicators of the presences of the classical/quantum correlations, respectively. The maximum bounds of the quantum and the classical correlations depend on the purity of the initial GHZ state. The classical correlation that depicted by the behavior of Wigner function independent of the acceleration, but depends on the degree of its purity.