The automatic modulation classification (AMC) of a detected signal has gained considerable prominence in recent years owing to its numerous facilities. Numerous studies have focused on feature-based AMC. However, improving accuracy under low signal-to-noise ratio (SNR) rates is a serious issue in AMC. Moreover, research on the enhancement of AMC performance under low and high SNR rates is limited. Motivated by these issues, this study proposes AMC using a feature clustering-based two-lane capsule network (AMC2N). In the AMC2N, accuracy of the MC process is improved by designing a new two-layer capsule network (TL-CapsNet), and classification time is reduced by introducing a new feature clustering approach in the TL-CapsNet. Firstly, the AMC2N executes blind equalization, sampling, and quantization in trilevel preprocessing. Blind equalization is executed using a binary constant modulus algorithm to avoid intersymbol interference. To extract features from the preprocessed signal and classify signals accurately, the AMC2N employs the TL-CapsNet, in which individual lanes are incorporated to process the real and imaginary parts of the signal. In addition, it is robust to SNR variations, that is, low and high SNR rates. The TL-CapsNet extracts features from the real and imaginary parts of the given signal, which are then clustered based on feature similarity. For feature extraction and clustering, the dynamic routing procedure of the TL-CapsNet is adopted. Finally, classification is performed in the SoftMax layer of the TL-CapsNet. This study proves that the AMC2N outperforms existing methods, particularly, convolutional neural network(CNN), Robust-CNN (R-CNN), curriculum learning(CL), and Local Binary Pattern (LBP), in terms of accuracy, precision, recall, F-score, and computation time. All metrics are validated in two scenarios, and the proposed method shows promising results in both.