A directional sensor network is formed by directional sensors which may be oriented toward different directions. The sensing region of a directional sensor can be viewed as a sector in a two-dimensional plane. Therefore, a directional sensor can only choose one sector (or direction) at any time instant. Planning of directional sensor networks has received very little attention in the literature. In this paper, we discuss directional sensor placement which is a critical task in the planning of directional sensor networks. We also present an integer linear programming model whose goal is to minimize the number of directional sensors that need to be deployed to monitor a set of discrete targets in a sensor field. Numerical results demonstrate the viability and effectiveness of the model.