Grey theory is an approach that can be used to construct a model with limited samples to provide better forecasting advantage for short-term problems. In some cases, a grey forecasting model may yield unacceptable forecasting errors. In this work, a new exponential grey prediction model, which is called as EXGM (1,1), is proposed. By using this model, new cases, deaths and recovered cases of COVID-19 in Turkey is forecast. Numerical results show that EXGM (1,1) is a model that performs more accurately than the comparison models.