A novel and extremely accurate near Gaussian approximation for the fundamental mode in single-mode optical fibers having arbitrary index profile is proposed and verified. The spot sizes calculated from present function matches exactly with the anahtical and exact numerical results for step and parabolic index fibers respectively over a practical range of values of normalised frequency V. For low V region, where Gaussian approximation is not faithful, it will be suitable to predict accurately the propagation characteristics of devices like directional coupler involving evanescent field coupling.