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The Weibel instability in the unmagnetized plasma system with arbitrary degeneracy anisotropic Fermi distribution is presented based on the Vlasov—Maxwellian kinetic theory.The result of non-degenerated limit is obtained to aid comparison with that of the Maxwellian.For the arbitrary degeneracy case,the numerical analysis is used and the growth rate is obtained,which may be responsible for the next—generation intense laser-solid density plasma experiments.It is shown that the some properties of Weibel instability obtained from the classical kinetic theory differ from that one from quantum kinetic theory.