Convolutional neural network (CNN) architectures have been extensively utilized in data-driven fault diagnosis and have demonstrated significant success. However, there remain certain constraints or restrictions of standard CNN for real-world applications, including discrete convolutions with a priori kernel size that failed to capture richer long-term features, performance deterioration when testing on irregular-length signals, and low accuracy under imbalanced datasets with severe levels of noise. In this paper, a new deep continuous convolutional network (DCCN) based on implicit neural representations is proposed to alleviate these limitations. Multilayer perceptrons with Gaussian masks are developed for the parameterization of continuous convolutional kernels, while multiplicative Gabor filters are used to improve the anti-noise ability. Depth-wise separable convolutions with residual connections are used to improve the computational efficiency of DCCN. The feasibility of DCCN has been verified on two laboratory datasets and one public dataset. The proposed approach achieves average macro F1-scores of over 98.69 % for bearing, gearbox, and mixed fault diagnosis under different noise interferences. Moreover, DCCN achieves an average macro F1-score of 86.43 % when training on 2048 data points and testing on 512 data points. Results show that DCCN has more robust recognition and anti-noise capability than state-of-art methods.