The desire to remedy the poor performance and inflexible system of bureaucratic in significant areas of the public sector, the increase sense of responsibility from political and administrative actors towards the citizen, stimulated changes in the public sector in the 80's and 90's. Cross-functional teams is a management tool with several organizational function capable of generating innovation. Its concept is a group of people with training, knowledge and varied experiences in order to harmonize knowledge to achieve a goal. The main objective of this research is to study how occurs innovation through cross-functional teams (CFT) in public sector organizations. This study was conducted in Secretaria da Fazenda do Estado de Minas Gerais. The selection of respondents was conducted by the indication of management and employee predisposition to participate in the interview being conducted 25 interviews. One aspect that stood out in the research accomplished was the lack of scientific studies with subjects treated in this work. This study finds points of contact between the themes functional teams, innovation and public sector showing how functional teams influence the processes in public administration, besides indicating unique characteristics of cross-functional teams of these organizations. The results found in the study indicates that predominates organization is the functional teams of the formal type with permanent duration and participation of temporary members in developing the project. The specialty at work is the main issues across the selection of members, this topic had a relationship with the kind of innovation produced. Also noteworthy is that the responsibility for innovation is from top to bottom for formal CFT, while the informal CFT occurs from the bottom up. As the role of the manager as well as being one of the main ways to promote the effective participation of team members and the active involvement of the same in the process, the survey indicated that the evaluation team conducted by management occurs simply whether or not the goal or proposed task. It was evident as the CFT can influence processes in Public Administration generating innovation with productivity gains. The research has extended the perspective of IPD in the public sector in the literature studied by detecting not only the generation of innovation, but also cases that form teams with people from other public and private organizations, increasing cross-functional integration.