The control of complex networks has been studied extensively in the last decade, with different control models been introduced. In this paper, we propose a new network control framework, called local controllability. Local controllability extends the entire network control onto a local scale, and it concerns about the minimum number of inputs required to control a subset of nodes in a directed network. We develop a mathematical formulation for local controllability as an optimization problem and show that it can be solved by a cubic-time algorithm. Moreover, applications to both real networks and model networks are presented and results of these numerical studies are then discussed.