Reliable and high precision multi-step ahead probabilistic forecasting of runoff can provide information for reservoir operation and decision-making. This study focuses on relying only on historical precipitation and evaporation data to complete the multi-step ahead forecasting, improving the runoff prediction accuracy, and quantifying the forecasting uncertainty. Firstly, the maximum translational Pearson Correlation Coefficient method is used to analyze the lag time of flow evolution from upstream station to downstream station. Then, the upstream, downstream, tributary historical runoff and interval historical precipitation and evaporation variables are constructed as three-dimensional tensors. Moreover, a deterministic forecasting model based on Convolutional Single Control Memory (ConvSCM) Neural Network is proposed. Furthermore, the probabilistic forecasting model BConvSCM is obtained by combining ConvSCM with the variational Bayesian framework. Finally, the model proposed in this study is applied to the middle and lower reaches of Yangtze River Basin. The experimental results and conclusions are as follows: (1) In the absence of rainfall forecasting data, the conceptual hydrological forecasting model can only complete single-step ahead forecasting, while the BConvSCM model can complete multi-step ahead forecasting. (2) The average determination coefficient of BConvSCM model’s mean predictions is 2.86% higher than that of traditional conceptual hydrological model, and 0.68% higher than that of existing deep learning model. And BConvSCM model can forecast suitable probability density function of runoff. The research results can provide reference for multi-step ahead probabilistic forecasting of runoff.