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In the scenarios of non-cooperative wireless communications, automatic modulation recognition (AMR) is an indispensable algorithm to recognize various types of signal modulations before demodulation in many internet of things applications. Convolutional neural network (CNN)-based AMR is considered as one of the most promising methods to achieve good recognition performance. However, conventional CNN-based methods are often unstable and also lack of generalized capabilities under varying noise conditions, because these methods are merely trained on specific dataset and can only work at the corresponding noise condition. Hence, it is hard to apply these methods directly in practical systems. In this paper, we propose a CNN-based robust automatic modulation recognition (RAMR) method to recognize three types of modulation signals, i.e., frequency shift key (FSK), phase shift key (PSK), and quadrature amplitude modulation (QAM). The proposed method is trained on a mixed dataset for extracting common features under varying noise scenarios. Simulation results show that our proposed generalized CNN-based architecture can achieve higher robustness and convenience than conventional ones.