Grossman and Katz (five decade ago) suggested a new definition of differential and integral calculus which utilize the multiplicative and division operator as compared to the addition and subtraction. Multiplicative Calculus is a vital part of the applied Mathematics because of its application in the area of Biology, Science and Finance, Biomedical, Economic, etc. Therefore, we used a multiplicative calculus approach to develop a new fourth-order iterative scheme for multiple roots based on the well-known King’s method. In addition, we also propose the detailed convergence analysis of our scheme with the help of multiplicative calculus approach rather than the normal one. Different kinds of numerical comparisons has been suggested and obtained results are very impressive as compared to the ordinary derivative methods. Finally, the convergence of our technique is also analyzed by basin of attractions that also support the theoretical aspects.