The World Health Organization has declared that the new Coronavirus disease (Covid-19) has become a pandemic since March 2020. It consists of an emerging viral infection with respiratory swelling that can progress to atypical pneumonia. In fact, experts stress the early detection importance of those infected with COVID-19 virus. In this way, the infected patients will be isolated from others, and then prevent the virus spread. However, prompt assessment of breathing patterns is important for many medical emergencies. We present, in this paper, a deep learning technique-based COVID-19 cough and breath analysis that can recognize positive COVID-19 cases from both negative and healthy COVID-19 cough and breath recorded on smartphones or wearable sensors. Firstly, audio signals, as well as cough and breath, will be preprocessed to remove noise. After that, deep features will be extracted using the deep Long Term Short Memory (LSTM) model. Finally, the recognition step will be performed exploiting extracted audio features. Numerical results prove the efficiency of the proposed deep model in terms of high accuracy level and low loss value compared to the other techniques.