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The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection.Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered.Next the authors study ζ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection.Furthermore,the authors study P-Sasakian manifolds satisfying the condition (Z)(ζ,Y) · (S) =0,where Z,S are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection.Finally,an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.