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Magneto-plasma loops,which trace closed solar magnetic field lines,are the primarystructural elements of the solar corona.Kinetic Alfvén wave (KAW) can play an important role ininhomogeneous heating of these magneto-plasma structures in the corona.By the use of alow-frequency kinetic dispersion equation,which is presented in this paper and is valid in afinite-β plasma with Q<β<1 plasma (where β is the kinetic to magnetic pressure ratio and Q =me /mi is the mass ratio of electrons to ions),KAW instability driven by a field-aligned current inthe current-carrying loops in the solar corona is investigated.The results show that the KAWinstability can occur in wave number regimes 0
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