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Deep neural networks have achieved great success in computer vision, speech recognition and many other areas. The potential of recurrent neural networks especially the Long Short-Term Memory (LSTM) for open set communication signal modulation recognition is investigated in this letter. Time-domain sampled signals are first converted to two normalized matrices which will be fed into a four layer Dual-Channel LSTM network tailored for open set modulation recognition. With two cascaded Dual-Channel LSTM layers, the designed network can automatically learn sequence-correlated features from the raw data. With center loss and weibull distribution, proposed algorithm can recognize partial open set modulations. Experiments on the public RadioML dataset indicates that different analog and digital modulations can be effectively classified by the proposed model, while partial open set modulations can be recognized. Quantitative analysis on the dataset shows that the proposed method can achieve an average accuracy of 90.2% at varying SNR ranging from 0dB to 18dB in classifying the considered 11 classes, while accuracy of open set experiment dramatically improved by 14.2%.