A theoretical model to explain the Freedericksz transition for a nematic liquid crystal with graphene quantum dots adding in electric field below the instability area is proposed. A mathematical formula for the critical voltage was obtained by elastic continuum theory combined with Burilov-Zakhlevnykh anchoring model, classical electrostatic principles and temperature dependence of elastic constant. We compared the results with the experimental data recorded for three LC samples and a good agreement between them was found encouraging us to propose this model as a tool for theoretical analysis of graphene quantum dot's dispersions in liquid crystals.