Acoustic Event Classification (AEC) has become a significant task for machines to perceive the surrounding auditory scene. However, extracting effective representations that capture the underlying characteristics of the acoustic events is still challenging. Previous methods mainly focused on designing the audio features in a `hand-crafted' manner. Interestingly, data-learnt features have been recently reported to show better performance. Up to now, these were only considered on the frame level. In this article, we propose an unsupervised learning framework to learn a vector representation of an audio sequence for AEC. This framework consists of a Recurrent Neural Network (RNN) encoder and an RNN decoder, which respectively transforms the variable-length audio sequence into a fixed-length vector and reconstructs the input sequence on the generated vector. After training the encoder-decoder, we feed the audio sequences to the encoder and then take the learnt vectors as the audio sequence representations. Compared with previous methods, the proposed method can not only deal with the problem of arbitrary-lengths of audio streams, but also learn the salient information of the sequence. Extensive evaluation on a large-size acoustic event database is performed, and the empirical results demonstrate that the learnt audio sequence representation yields a significant performance improvement by a large margin compared with other state-of-the-art hand-crafted sequence features for AEC.