Sleep staging is one of the important methods for the diagnosis of the different types of sleep-related diseases. Manual inspection of sleep scoring is a very time-consuming process, labor-intensive, and requires more human interpretations, which may produce biased results. Therefore, in this paper, we propose an efficient automated sleep staging system to improve sleep staging accuracy. In this work, we extracted both linear and non-linear properties from the input signal. Next to that, a set of optimal features was selected from the extracted feature vector by using a feature reduction technique based on the ReliefF weight algorithm. Finally, the selected features were classified through four machine learning techniques like support vector machine, K-nearest neighbor, decision tree, and random forest. The proposed methodology performed using dualchannel EEG signals from the ISRUC-Sleep dataset under the AASM sleep scoring rules. The performance of the proposed methodology compared with the existing similar methods. In this work, we considered the 10-Fold cross validation strategy; our proposed methods reported the highest classification accuracy of 91.67% with the C4-A1 channel, and 93.8% with the O2-A1 channel using the Random forest classification model. The result of the proposed methodology outperformed the earlier contribution for two-class sleep states classification. The proposed dual-channel sleep staging method can be helpful for the clinicians during the sleep scoring and treatment for the different sleep-related diseases.