Spatio-temporal series prediction has attracted increasing attention in the field of meteorology in recent years. The spatial and temporal joint effect makes predictions challenging. Most of the existing spatio-temporal prediction models are computationally complicated. To develop an accurate but easy-to-implement spatio-temporal prediction model, this paper designs a novel spatio-temporal prediction model based on echo state networks. For real-world observed meteorological data with randomness and large changes, we use a cubic spline method to bridge the gaps between the neighboring points, which results in a pleasingly smooth series. The interpolated series is later input into the spatio-temporal echo state networks, in which the spatial coefficients are computed by the elastic-net algorithm. This approach offers automatic selection and continuous shrinkage of the spatial variables. The proposed model provides an intuitive but effective approach to address the interaction of spatial and temporal effects. To demonstrate the practicality of the proposed model, we apply it to predict two real-world datasets: monthly precipitation series and daily air quality index series. Experimental results demonstrate that the proposed model achieves a normalized root-mean-square error of approximately 0.250 on both datasets. Similar results are achieved on the long short-term memory model, but the computation time of our proposed model is considerably shorter. It can be inferred that our proposed neural network model has advantages on predicting meteorological series over other models.