A social network is a social structure with a set of social actors and other social interactions between actors. The social network supports a set of methods to explain the structure of whole social entities as well as a variety of theories in these structures. The study of these structures uses social network analysis to explain local and global patterns and examine network dynamics. The related economic data is important for our economic developments. We could analyze the economic data to explore the investments. In this paper, we focus on the design and analysis of automatic management systems to make a decision about the petroleum projects. Petroleum is the lifeblood of economic development. So, we need an automatic and effective management system to make the mining investments of petroleum. Before deciding to invest in the petroleum project, the engineers will describe this project by providing the sufficient economic data. Based on this data, the decision can undertake professional analysis, to determine whether the project is feasible. To automate the manual process and overcome the traditional evaluation method, the BP (back propagation) neural network is applied in a petroleum project economic evaluation. This method opens up a new way for the evaluation of petroleum projects. In this article, we first introduce the application of BP neural network. Then, we introduce the principle and shortcoming of BP neural network. Based on it, we optimize the BP neural network. Secondly, according to the characteristics of petroleum projects, we obtain the economic evaluation indicators about petroleum projects, which are used as the input of the BP neural network. Thirdly, we propose the design of the BP neural network and select the smallest simulation error of the BP neural network as a forecasting model of petroleum projects. In order to improve the accuracy, the labeled training samples are selected for BP neural network training. Finally, based on extensive simulation experimental results, we demonstrate our scheme about the BP neural network of petroleum project evaluation is effective and has overperformance than traditional schemes in terms of convenience and accurate decision-making suggestions.