The asymptotic iteration method (AIM) has been applied to calculate the ground state and binding energy of an impurity located at the center of a single and multilayered spherical quantum dot.Regarding the single quantum dot (QD) the results obtained for the ground state energy and for the first approximation of the binding energy agree entirely with the results of the ordinary perturbation technique obtained in earlier treatments. Besides, the second approximation of the binding energy differs by about 16.5 % in both treatments which is quite reasonable. The results obtained in the case of multilayered spherical quantum dot (MSQD) showed a reasonable quantitative agreement with the results obtained in an earlier treatment by applying an entire numerical technique. They are also distinguished by exhibiting a peak similar to the results obtained before by applying the variational method in analogous problems.