Objective: The purpose of the present study is to discuss the stability of a thermo-convective problem where the gravity field varies across the layer under the influences of internal heat source and rotation when both the boundary surfaces are free. Methods: Linear stability analysis is performed to discuss the stability of the problem and the associated eigen-value problem is solved by using Newton-Raphson method. Results: The numerical approximations of the Rayleigh number are obtained for various values of the parameters and presented in tables 1 and 2. Numerical results show a destabilizing effect of the presence of heat source. Comparisons with the available published work are also presented. Conclusion: It is found that the critical Rayleigh number increases with an increase in gravity field and decrease in heat source i.e. the region of stability decreases with an increase in heat source.