Software requirement smell detection is an important part of establishing high-quality software specifications. These smells, which frequently indicate difficulties like ambiguity, vagueness, or incompleteness, can lead to misunderstandings and mistakes in the latter phases of software development. Traditionally, identifying requirement smells was a manual process, time-consuming, prone to inconsistency, and human mistakes. Moreover, the previous machine learning and deep learning research was insufficient for detecting multiple smells in a single requirement statement. To address this problem, we developed a multi-label software requirement smell model to detect multiple software requirement smells in a single requirement. Therefore, this study explores a deep learning-based approach to multi-label classification of software requirement smells, incorporating advanced neural network architectures such as LSTM, Bi-LSTM, and GRU with combined word embedding like ELMo and Word2Vec. We collected and prepared an 8120 requirements dataset from different sources categorized into 11 linguistic aspects and we used a binary relevance multi-label classification strategy in which each category was treated independently and used the F1-macro average of each label of the smell. Next, we built models that can classify software requirement smell in a multi-label manner using deep learning algorithms. After executing numerous experiments with different parameters in the Bi-LSTM, LSTM, and GRU models, we obtained 90.3%, 89%, and 88.7% of F1-score macro averages with ELMo, respectively. Therefore, Bi-LSTM achieved a greater F1-score macro average than the other algorithms.