Automatic classification of cell types and biological products are considered crucial in the field of hematology especially for early detection of diseases when the quantity that needs to be examined is considerably large. In a previous study, a cylindrical micro-channel was employed to mimic actual blood flow in the arteriole but it was found to cause astigmatism in the reconstructed holographic particle images. Additionally, correction of the images is important to avoid false disease detection. In this paper, we describe a new application of feed-forward backpropagation neural network for classifying images of astigmatic and non-astigmatic synthetic platelets that were obtained by digital holographic microscopy. Image cropping was performed to suppress noise, followed by image normalization to reduce variation in contrast/brightness. Using MATLABTM, a two-layer neural network with two class classifier was trained with these images to compute the weights of each layer and the performance was benchmarked against three performance indices. The results show that the present method was able to classify 1050 platelet images with 100% recognition rate for Class 1 (non-astigmatic) and 71.4% recognition rate for Class 2 (astigmatic). The trained neural network was then applied to a set of 9000 images. Finally, digital aberration correction by complex-amplitude correlation was successfully applied to correct for the astigmatism.