A parallel text corpus is an important resource for building a machine translation (MT) system. Existing resources such as translated documents, bilingual dictionaries, and translated subtitles are excellent resources for constructing parallel text corpus. A sentence alignment algorithm automatically aligns source sentences and target sentences because manual sentence alignment is resource-intensive. Over the years, sentence alignment approaches have improved from sentence length heuristics to statistical lexical models to deep neural networks. Solving the alignment problem as a classification problem is interesting as classification is the core of machine learning. This paper proposes a parallel long-short-term memory with attention and convolutional neural network (parallel LSTM+Attention+CNN) for classifying two sentences as parallel or non-parallel sentences. A sliding window approach is also proposed with the classifier to align sentences in the source and target languages. The proposed approach was compared with three classifiers, namely the feedforward neural network, CNN, and bi-directional LSTM. It is also compared with the BleuAlign sentence alignment system. The classification accuracy of these models was evaluated using Malay-English parallel text corpus and UN French-English parallel text corpus. The Malay-English sentence alignment performance was then evaluated using research documents and the very challenging Classical Malay-English document. The proposed classifier obtained more than 80% accuracy in categorizing parallel/non-parallel sentences with a model built using only five thousand training parallel sentences. It has a higher sentence alignment accuracy than other baseline systems.