Mental task identification using electroencephalography (EEG) signals is required for patients with limited or no motor movements. A subject-independent mental task classification framework can be applied to identify the mental task of a subject with no available training statistics. Deep learning frameworks are popular among researchers for analyzing both spatial and time series data, making them well-suited for classifying EEG signals. In this paper, a deep neural network model is proposed for mental task classification for an imagined task from EEG signal data. Pre-computed features of EEG signals were obtained after raw EEG signals acquired from the subjects were spatially filtered by applying the Laplacian surface. To handle high-dimensional data, principal component analysis (PCA) was performed which helps in the extraction of most discriminating features from input vectors. The proposed model is non-invasive and aims to extract mental task-specific features from EEG data acquired from a particular subject. The training was performed on the average combined Power Spectrum Density (PSD) values of all but one subject. The performance of the proposed model based on a deep neural network (DNN) was evaluated using a benchmark dataset. We achieved 77.62% accuracy. The performance and comparison analysis with the related existing works validated that the proposed cross-subject classification framework outperforms the state-of-the-art algorithm in terms of performing an accurate mental task from EEG signals.