Stability characteristics of a laminar natural convection flow above a horizontal line heat source are theoretically investigated on the basis of the linear stability theory. The coupled Orr-Sommerfeld equations are integrated numerically for anti-symmetric disturbances. The contours for various amplification rates are obtained in the Grashof number-wavenumber and the Grashof number-frequency diagrams. The eigenfunctions for the velocity and temperature disturbances are also calculated. Experiments are carried out for verifying the above-obtained theoretical results. All the experimental results are found to be in good agreement with them. A phenomenon called swaying motion, which was already reported in previous papers, seems to be explicable within the scope of the linear stability theory developed in the present paper.