Open banking brings both the opportunities and challenges to banks all over the world. Due to the different economic development levels of each country and the gaps among financial environment maturity, all countries have different strategies and regulations towards the privacy protection of data in financial scenes, such as the General Data Protection Regulation (GDPR) by European Union (EU). A blockchain as a continuously growing list of records managed by a peer-to-peer network is widely used in various application scenarios, and can protect the privacy of financial data. However, financial blockchain still poses some problems that cannot fully meet the data protection needs. In order to address the existing problems, this paper proposes a new blockchain-based data privacy management framework. The framework consists of three components: a data privacy classification method according to the characteristics of financial data and a new collaborative-filtering-based model and a confirmation data disclosure scheme for customer strategies based on the Nudge Theory. We implement a prototype and propose a set of algorithms for this management framework.