Epilepsy is a chronic nervous disorder, which disturbs the normal daily routine of an epileptic patient due to sudden seizure onset. In this era of smart healthcare, automated seizure prediction techniques could assist the patients, their family, and medical personnel to control and manage these seizures. This paper proposes a spectral feature-based two-layer LSTM network model for automatic prediction of epileptic seizures using long-term multichannel EEG signals. This model makes use of spectral power and mean spectrum amplitude features of delta, theta, alpha, beta, and gamma bands of 23-channel EEG spectrum for this task. Initially, the proposed single-layer and two-layer LSTM models have been evaluated for EEG segments having durations in the range of 5–50 s for 24 epileptic subjects, out of which EEG segments of 30 s duration are found to be useful for accurate seizure prediction using two-layer LSTM model. Afterwards, to validate the performance of this classifier, the spectral features of 30 s duration EEG segments are fed to random forest, decision tree, k-nearest neighbour, support vector machine, and naive Bayes classifiers, which are empowered with grid search-based parameter estimation. Finally, the iterative simulation results and comparison with recently published existing techniques firmly reveal that the proposed two-layer LSTM model with EEG spectral features is an effective technique for accurately predicting seizures in real time with an average classification accuracy of 98.14%, average sensitivity of 98.51%, and average specificity of 97.78%, thereby enabling the epileptic patients to have a better quality of life.