Detecting moving objects is one of the most important research interest at present in computer vision due to its wide range of applications in traffic surveillance, human motion analysis and object tracking. Some approaches such as Gaussian running average provides faster background subtraction for object detection. However, it considers a fixed threshold for the background subtraction, which limits its application. In this research, a modification of Gaussian average technique has been proposed with the aid of an adaptive threshold and learning rate for traffic surveillance. The proposed approach develops a background model dynamically by extracting the edge information of individual frame. The application of adaptive threshold and learning rate over Gaussian average makes the approach more robust and suitable for video surveillance applications. The proposed approach has been tested on the real-time traffic data captured on a busy street using fixed camera. With the proposed technique, the moving vehicles are detected more accurately with little noise. The experimental results presented at the end reflect the suitability of the approach.