Prediction of the blood flow characteristics is of utmost importance for understanding the behavior of the blood arterial network, especially in the presence of vascular diseases such as stenosis. Computational fluid dynamics (CFD) has provided a powerful and efficient tool to determine these characteristics including the pressure and velocity fields within the network. Despite numerous studies in the field, the extremely high computational cost of CFD has led the researchers to develop new platforms including Machine Learning approaches that instead provide faster analyses at a much lower cost. In this study, we put forth a Deep Neural Network framework to predict flow behavior in a coronary arterial network with different properties in the presence of any abnormality like stenosis. To this end, an artificial neural network (ANN) model is trained using synthetic data so that it can predict the pressure and velocity within the arterial network. The data required to train the neural network were obtained from the CFD analysis of several geometries of arteries with specific features in ABAQUS software. Blood pressure drop caused by stenosis, which is one of the most important factors in the diagnosis of heart diseases, can be predicted using our proposed model knowing the geometrical and flow boundary conditions of any section of the coronary arteries. The efficiency of the model was verified using three real geometries of LAD's vessels. The proposed approach precisely predicts the hemodynamic behavior of the blood flow. The average accuracy of the pressure prediction was 98.7% and the average velocity magnitude accuracy was 93.2%. According to the results of testing the model on three patient-specific geometries, model can be considered as an alternative to finite element methods as well as other hard-to-implement and time-consuming numerical simulations.