Deep learning has recently attracted much attention due to its excellent performance in processing audio, image, and video data. However, few studies are devoted to the field of automatic modulation classification (AMC). It is one of the most well-known research topics in communication signal recognition, which remains challenging for traditional methods due to the complex disturbance from other sources. This paper proposes a heterogeneous deep model fusion (HDMF) method to solve the problem in a unified framework. The contributions include: 1) The convolutional neural network (CNN) and long short-term memory (LSTM) are combined by two different ways without prior knowledge involved; 2) A large database, including eleven types of single-carrier modulation signals with various noises as well as a fading channel, is collected with various signal-to-noise ratios (SNRs) based on a real geographical environment; and 3) Experimental results demonstrate that HDMF is super capable of copping with the AMC problem, and achieves much better performance when compared with the independent network. The source code and the database will be publically available.