The Fermi contact term has a close relationship with the atomic hyperfine constants. It often dominates the hyperfine splittings. The quality of the wave function near the origin and the correlation effect between electrons are two main factors which affect the numerical accuracy of the Fermi contact term. It is not an easy task to compute the Fermi contact term to high precision for a general atom. In the present paper, the Schrödinger equation of the ,

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... 1<i>s</i>2<i>s</i>3<i>s</i>⁴S and 1<i>s</i>2<i>s</i>2<i>p</i>⁴P states of lithium atom and lithium-like ions (Z=4-10) are solved using Rayleigh-Ritz variational method in Hylleraas coordinates. The variational energies converge to an accuracy of 10^-13. Then the Fermi contact terms for these states are calculated based on the high precision variation wave functions. In particular, the Drachman global method are resorted in order to improve the convergence of the Fermi contact term. The effect of finite nuclear mass on Fermi contact term, i.e., the first-order mass polarization coefficients are also calculated. The Fermi contact terms converge to an accuracy of 10^-10, which are the most accurate results at present. Our results can be used as a reference for other theoretical methods or relevant experimental studies.