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In this paper a relativistic many-body perturbation calculation is performed to calculate the hyperfine constants of the ground states for lithium-like isoelectronic sequence. Zeroth-order hyperfine constants are calculated with Dirac-Fock wavefunctions, and the finite basis sets of the Dirac-Fock equations are constructed by B splines. With the finite basis sets, the core polarization and the correlation effect are evaluated.