Landau damping is a phenomena observed in plasma wherein there is an exponential decay in the oscillations of the number density of electrons in a plasma, Collisionless damping of electrical waves in plasma is investigated in the frame of the classical formulation of the problem. The effect of variable dust size and charge on the Landau damping of acoustic waves is studied in presence of hybrid nontheremal nonextensive electrons. Based on the kinetic theory, landau damping of dust acoustic waves (DAWs) propagating characteristics in a dusty plasma with negatively charged dust grains and Maxwellian ion distribution is investigated using Vlasov – Poisson`s equations. The charging of dust grains is described by the orbital-motion-limited theory and the size of the dust grains obeys the power law dust size distribution. the dependence of the wave frequency 𝜔 on the difference between the largest and the smallest dust radius for different wave numbers are plotted, also Phase diagram of the Landau damping as a function of both the grain radius of dusty plasma and the wave number are plotted, there are three different regions in the diagram.The present study is useful in the space situations where such distribution exists.