The automatic generation of a text summary is a task of generating a short summary for a relatively long text document by capturing its key information. In the past, supervised statistical machine learning was widely used for the Automatic Text Summarization (ATS) task, but due to its high dependence on the quality of text features, the generated summaries lack accuracy and coherence, while the computational power involved, and performance achieved, could not easily meet the current needs. This paper proposes four novel ATS models with a Sequence-to-Sequence (Seq2Seq) structure, utilizing an attention-based bidirectional Long Short-Term Memory (LSTM), with added enhancements for increasing the correlation between the generated text summary and the source text, and solving the problem of out-of-vocabulary (OOV) words, suppressing the repeated words, and preventing the spread of cumulative errors in generated text summaries. Experiments conducted on two public datasets confirmed that the proposed ATS models achieve indeed better performance than the baselines and some of the state-of-the-art models considered.