This conceptual paper puts forward the construct termed "teacher curriculum competence," which is an amalgamation of theoretical or formal and personal practical teacher knowledge and orientations in relation to curriculum. We situate the competence in institutional, political, and philosophical contexts. Drawing on research related to mathematics curriculum at different stages (i.e. the official, intended, and enacted curriculum) and teacher competence frameworks, we elaborate on how a teacher interacts with curriculum informed by their knowledge and orientations. When working with curriculum, teacher curriculum competence refers to "what" teachers attend to and "how" they interpret curriculum, as well as "why" they make decisions, including "when" to introduce particular concepts or skills, based on their local students' needs. In addition, we argue that the process of interacting with curriculum helps shape teacher knowledge and orientations. This article is significant for the contribution it makes to conceptualizing teacher curriculum competence in a centralized curriculum system, that is a nationally mandated. Although we use the mathematics discipline as an example, implications for research in promising areas for future studies in this space are also discussed.