Nuclear level density (NLD) is a characteristic property of many-body quantum mechanical systems. NLDs are of special importance to make statistical calculations in reactor studies and various theoretical and experimental nuclear physics and engineering applications. In this study, we have investigated a set of particle states in distinct rotational and vibrational bands to calculate nuclear level density parameters and the NLDs of accessible states of some deformed Dy radionuclides using a collective model approach, which included different excitation bands of the observed nuclear spectra. The method used assumes equidistant spacing of collective coupled state bands of the considered nuclei. The results of the calculated NLD have been compared with the experimental and compiled data obtained by the Oslo group, shell model Monte Carlo, Hartree-Fock-Bogoliubov + combinatorial approach, Bardeen-Cooper-Schrieffer approach and are in a good agreement.