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We discuss Bianchi type-Ⅶ0 cosmology with a Dirac field in the Einstein-Cartan(E-C) theory and obtain the equations of the Dirac and gravitational fields in the E-C theory.A Bianchi type-Ⅶ0 inflationary solution is found.When(3/16)S2-σ2>0, the Universe may avoid singularity.