Time-series data is an appealing study topic in data mining and has a broad range of applications. Many approaches have been employed to handle time series classification (TSC) challenges with promising results, among which deep neural network methods have become mainstream. Echo State Networks (ESN) and Convolutional Neural Networks (CNN) are commonly utilized as deep neural network methods in TSC research. However, ESN and CNN can only extract local dependencies relations of time series, resulting in long-term temporal data dependence needing to be more challenging to capture. As a result, an encoder and decoder architecture named LA-ESN is proposed for TSC tasks. In LA-ESN, the encoder is composed of ESN, which is utilized to obtain the time series matrix representation. Meanwhile, the decoder consists of a one-dimensional CNN (1D CNN), a Long Short-Term Memory network (LSTM) and an Attention Mechanism (AM), which can extract local information and global dependencies from the representation. Finally, many comparative experimental studies were conducted on 128 univariate datasets from different domains, and three evaluation metrics including classification accuracy, mean error and mean rank were exploited to evaluate the performance. In comparison to other approaches, LA-ESN produced good results.