One of the most widely used frameworks for image-based sequence recognition is the convolutional recurrent neural network, which uses a convolutional neural network (CNN) for feature extraction and a recurrent neural network (RNN) for sequence modeling. However, the RNN is computationally expensive in both training and inference, which limits its application in time-constrained systems. Some models replace the RNN with an attention mechanism for sequence modeling but still, require expensive iterative computations. In this paper, we argue that a CNN with sufficient depth can capture contextual information, eliminate the need for recurrent operations and thus be fully parallelized. We focus on the problem of water meter number reading (WNR), which is a typical sequence recognition task but has rarely been investigated. We propose a fully convolutional sequence recognition network (FCSRN) for the fast and accurate reading of water meter numbers. Furthermore, we design an augmented loss (AugLoss) function to manage the intermediate states of the digits and effectively improve performance. The experimental results demonstrate that the FCSRN has the ability to capture contextual information and eliminate the need for recurrent layers, and simultaneously requires fewer parameters and less computation. The FCSRN with AugLoss outperforms RNN-based and attention-based models. In addition, AugLoss can effectively improve the performance for RNN-based and attention-based models. Moreover, we constructed and released a dataset that contains 6000 water meter images with labels