Motor imagery (MI) based brain-computer interface (BCI) facilitates a medium to translate the human motion intentions using Motor imagery electroencephalogram (EEG) into control signals. A major challenge in BCI research is the identification of non-stationary brain electrical signals to categorize human motion intentions. We propose a novel method based on wavelet envelope analysis and long-term short-term memory (LSTM) classifier which consider the amplitude modulation characteristics and time series information of MI-EEG to classify EEG signals into multiple classes. First, the Hilbert transform (HT) and discrete wavelet transform (DWT) are combined to extract significant features which contains the underlying information of both amplitude modulation and frequency modulation of the EEG signals. Then, the wavelet envelope features are input into an LSTM classifier with input gates, forget gates, and output gates for classification. Finally, the experiment was conducted on the 2003 BCI competition data set III with 5-fold cross-validation, and experimental results show that the proposed method helps achieve higher classification accuracy.