An attempt is given for calculating the thermodynamical quantities with respect to the vibrational frequencies of the imperfect lattices. Using the method of contour integral the expressions for the difference of vibrational free energies between imperfect and perfect lattices are derived. These are given in two forms available at high and at low temperatures. As the examples of the practical calculations using these formulae, the n-dimensional simple lattices with defects are treated. Especially the simple cubic lattice as well as the linear chain are investigated in detail. Although in this example a simplified model of the actual defect is considered, it may be enough to discuss the general features of the thermodynamical properties of the imperfect lattices.