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We apply the nonextensive statistical theory given by Landau and Lifshitz to study the stability condition of convection in a fluid. When introducing Du's equation (Du J. L., Europhys. Lett., 67 (2004) 893), a relationship between the temperature gradient and the potential field of a nonequilibrium complex system by the nonextensive parameter, into the stability condition, we find that the nonextensive parameter can be used as the stability criterion of the convection taking place in a fluid. With the data of the standard solar models for BP2000 and BS2005, we apply this criterion to the solar interior and show a stability range from the center of the Sun to 0.74 R ,which is in excellent agreement with the helioseismological measurements inside the Sun. With the same data, the lower limit of the adiabatic index, when stability is needed, has been calculated.

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