The novel coronavirus (COVID-19) has significantly spread over the world and comes up with new challenges to the research community. Although governments imposing numerous containment and social distancing measures, the need for the healthcare systems has dramatically increased and the effective management of infected patients becomes a challenging problem for hospitals. Thus, accurate short-term forecasting of the number of new contaminated and recovered cases is crucial for optimizing the available resources and arresting or slowing down the progression of such diseases. Recently, deep learning models demonstrated important improvements when handling time-series data in different applications. This paper presents a comparative study of five deep learning methods to forecast the number of new cases and recovered cases. Specifically, simple Recurrent Neural Network (RNN), Long short-term memory (LSTM), Bidirectional LSTM (BiLSTM), Gated recurrent units (GRUs) and Variational AutoEncoder (VAE) algorithms have been applied for global forecasting of COVID-19 cases based on a small volume of data. This study is based on daily confirmed and recovered cases collected from six countries namely Italy, Spain, France, China, USA, and Australia. Results demonstrate the promising potential of the deep learning model in forecasting COVID-19 cases and highlight the superior performance of the VAE compared to the other algorithms.