Due to the rapid development of new technologies such as cloud computing, Internet of Things (IoT), and mobile Internet, the data volumes are exploding. Particularly, in the industrial field, a large amount of data is generated every day. How to manage and use industrial Big Data primely is a thorny challenge for every industrial enterprise manager. As an emerging form of service, cloud computing technology provides a good solution. It receives more and more attention and support due to its flexible configuration, on-demand purchase, and easy maintenance. Using cloud technology, enterprises get rid of the heavy data management work and concentrate on their main business. Although cloud technology has many advantages, there are still many problems in terms of security and privacy. To protect the confidentiality of the data, the mainstream solution is encrypting data before uploading. In order to achieve flexible access control to encrypted data, attribute-based encryption (ABE) is an outstanding candidate. At present, more and more applications are using ABE to ensure data security. However, the privacy protection issues during the key generation phase are not considered in the current ABE systems. That is to say, the key generation center (KGC) knows both of attributes and corresponding keys of each user. This problem is especially serious in the industrial big data scenario, because it will cause great damage to the business secrets of industrial enterprises. In this paper, we design a new ABE scheme that protects user's privacy during key issuing. In our new scheme, we separate the functionality of attribute auditing and key generating to ensure that the KGC cannot know user's attributes and that the attribute auditing center (AAC) cannot obtain the user's secret key. This is ideal for many privacy-sensitive scenarios, such as industrial big data scenario.