In the research paper, Klein Gordon Equation which is a non-linear partial differential equation of order two is discussed by using HS-3W method. A variety of physical phenomena are discussed in the field of Engineering and sciences by using this equation. Space and time approximation is done by using the proposed technique and converting the equation into system of algebraic equations and the non-linearities present in the equation is solved by using Quasilinearisation approach. To check the applicability of the method, proposed scheme is applied on various examples which shows the methods accuracy and compatibility with good results. By using MATLAB, graphical representation of exact, approximate solution and absolute error is shown.