Road accidents cause more than 1,35,000 deaths in India every year which is higher than any other country in the world. Increasing motorization without adequate institutional mechanism is a major cause of this problem. Although, the number of fatalities caused by road accidents in Delhi has been declining over the years, but the situation is still alarming. In this paper we use the back propagation neural network model for predicting the road accidents and fatalities caused by them in Delhi based on the number incidents of drunken driving, over speeding, driving without wearing seat belts and helmets and the number of vehicles registered in Delhi. The data of these traffic violations and year wise vehicle registration was collected for the years 2008 to 2012. Out of 5 data sets, 3 were used for training and 2 data sets were used for testing. The data was fed to a neural network of 1 hidden layer and another of 2 hidden layers consisting 11 nodes each. The lowest average error obtained was 6.3728 % for the neural network with a single hidden layer.