Electronic government (e-gov) is implemented in many countries as a way to improve the efficiency and effectiveness of service delivery in the public sector. One of the e-gov challenges concerns designing applications that meet the needs of citizen users while there is a low level of adoption of e-government services by citizens. User Experience (UX) is a quality of use criteria that represents a good interaction between users and interactive computer systems. The field of UX Design is precisely the institutionalization of UX, specifically at the government level. Just as governments need maturity models for their most effective implementation, they also need a UX eye for their software development projects. Many maturity models related to UX and usability have been proposed in the last decades, however the focus on describing the current maturity level of an organization, not helping the organization to advance to the next stage. In addition, the UX maturity models were designed for organizations in general, without a specific focus on e-government. Also these models are not specifically intended for Brazilian governments, in the most diverse areas (health, education, finance, etc.). In this sense, this work has the general objective of helping government organizations to increase their UX maturity by proposing a maturity model more focused on Brazilian UX and e-government. For this, we did a bibliographical research and investigated the current state of some Brazilian government agencies in relation to the adoption of UX in their projects. Then we proposed a UX maturity model for government institutions. Finally, we carried out action research in a Brazilian government organization to evaluate the proposed model.