Coronavirus is known as COVID-19. It spreads in all over the world as pandemic. Until writing this paper, 164.5 million person worldwide is affected with this disease. Over 3.4 million people are died due to that disease. Cough is one of the most common symptoms of that disease. The analysis of cough sounds of COVID-19 is applied using machine learning algorithm. The dataset is from open source COSWARA dataset. The applied algorithm can distinguish between positive and healthy subjects of COVID-19. Feature extraction from heavy cough sounds is applied by using new method which is called as bark wavelet cepstral coefficients (BWCC). This method is extracted from bark frequency cepstral coefficients (BFCC). The classification method is conducted using deep learning neural network (DLNN). The obtained accuracy percent using BWCC is 98.25% which overperform when using BFCC , mel frequency cepstral coefficients (MFCC) or mel wavelet cepstral coefficients (MWCC). So, BWCC is the best way for feature extraction of heavy cough sounds.