In December of 2019, a novel coronavirus (COVID-19) appeared in Wuhan city, China and has been reported in many countries with millions of people infected within only four months. Chest computed Tomography (CT) has proven to be a useful supplement to reverse transcription polymerase chain reaction (RT-PCR) and has been shown to have high sensitivity to diagnose this condition. Therefore, radiological examinations are becoming crucial in early examination of COVID-19 infection. Currently, CT findings have already been suggested as an important evidence for scientific examination of COVID-19 in Hubei, China. However, classification of patient from chest CT images is not an easy task. Therefore, in this paper, a deep bidirectional long short-term memory network with mixture density network (DBM) model is proposed. To tune the hyperparameters of the DBM model, a Memetic Adaptive Differential Evolution (MADE) algorithm is used. Extensive experiments are drawn by considering the benchmark chest-Computed Tomography (chest-CT) images datasets. Comparative analysis reveals that the proposed MADE-DBM model outperforms the competitive COVID-19 classification approaches in terms of various performance metrics. Therefore, the proposed MADE-DBM model can be used in real-time COVID-19 classification systems.