This paper presents a Gaussian Mixture Model (GMM) to identify the script of handwritten words of Roman, Devanagari, Kannada and Telugu scripts. It emphasizes the significance of directional energies for identification of script of the word. It is robust to varied image sizes and different styles of writing. A GMM is modeled using a set of six novel features derived from directional energy distributions of the underlying image. The standard deviation of directional energy distributions are computed by decomposing an image matrix into right and left diagonals. Furthermore, deviation of horizontal and vertical distributions of energies is also built-in to GMM. A dataset of 400 images out of 800 (200 of each script) are used for training GMM and the remaining is for testing. An exhaustive experimentation is carried out at bi-script, tri-script and multi-script level and achieved script identification accuracies in percentage as 98.7, 98.16 and 96.91 respectively.