A no-reference image quality assessment technique can measure the visual distortion in an image without any reference image data. Image distortions can be caused through the acquisition, compression or transmission of digital images. From the several types of image distortions, JPEG and JPEG2000 compression distortions, addition of white noise, Gaussian blur and fast fading are the most common ones. A typical real-world image may have multiple types of distortion. Our aim is to determine the different types of distortion that are present in an image and find the total distortion levels using a novel architecture using multiple Deep Convolutional Neural Networks (MDNN). The proposed model will classify different types of distortion that are present in an image thereby achieving both these objectives. Initially, local contrast normalization (LCN) is performed on images which are fed into the deep neural network for training. The images are then processed by a convolution-based distortion classifier which estimates the probability of each distortion type. Next, the distortion quality is predicted for each class. These probabilities are fused using the weighted average-pooling algorithm to get a single regressor output. We also experimented on the different parameters of the neural network, including optimizers (Adam, Adadelta, SGD, Rmsprop) and activation functions (RELU, SoftMax, Sigmoid, and Linear). The LIVE II database is used for the training, since it has five of the major distortion types. Cross-dataset validation is done on the CSIQ and TID2008 database. The results were evaluated using different correlation coefficients (SORCC, PLCC) and we achieved a linear correlation with the differential mean opinion scores (DMOS) for each of these coefficients in the tests conducted.