Cardiovascular diseases are one of the major causes of all human deaths. Irregular heartbeat or arrhythmia is one among many reasons for cardiovascular diseases. Arrhythmia detection and classification is critical in the treatment of irregular heartbeats. This paper presents a systematic method for high accuracy arrhythmia detection and classification using ArrhyNet, a custom convolutional neural network (CNN) for arrhythmia classification on MIT-BIH Arrhythmia Database. High and low frequency noise in the data is eliminated using low pass filter and baseline wander filter respectively, feature extraction is achieved using Daubechies Wavelet Transform and finally Synthetic Minority Over Sampling (SMOTE) technique is utilized to overcome the issue of imbalanced dataset. Using our technique, 16 different types of arrhythmias distributed in Association for Advancement of Medical Instrumentation (AAMI) standard were analyzed. The results indicate that the top-1 accuracy of our five-class classification system for the database used is 92.73%.