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The River Ganga (2,525 km long) is the largest River basin in India, covering 26.2 percent of India's total geographical area and recently granted living entity status by the court. It is the holiest River and also among the dirtiest in the world. That’s why it is mandatory to maintain its water quality (WQ). Though, monitoring and assessment of WQ of a River is a very challenging task. In this research work, Soft Computing (SC) based popular and commononly used Artificial Neural Network (ANN) technique has been used for modelling the WQ of the Ganga River by developing a prediction model based on six different training functions. Five sampling stations along this River stretch were selected from DEVPRAYAG to ROORKEE in the Uttarakhand state of India. The monthly data sets of five water quality parameters temperature, pH, dissolved oxygen (DO), biochemical oxygen demand (BOD) and total coliform (TC) for the time period from 2001 to 2015 have been taken. The feed forward error back propagation neural network method has been used to develop the WQ-prediction model by conducting various experiments following a neural network structure of 5-10-1, 0.1 as a training goal and various training functions. Using the Mean square error (MSE) statistical method the prediction performance of the developed model was evaluated. The model developed with traincgp (Conjugate Gradient with Polak-Ribiere Restarts) comes out to be the worst one (MSE=0.786) while the other model with trainlm (Levenberg-Marquardt backpropagation) rule proved to be the best one (MSE=0.163) among others. Consequently, it is found that ANNs are capable of predicting WQ of the River Ganga with acceptable results.