The ventral pathway in visual cortex is responsible for the perception of shape. Area V4 is an important intermediate stage in this pathway, and provides the major input to the final stages in inferotemporal cortex. The role of V4 in processing shape information is not yet clear. We studied V4 responses to contour features (angles and curves), which many theorists have proposed as intermediate shape primitives. We used a large parametric set of contour features to test the responses of 152 V4 cells in two awake macaque monkeys. Most cells responded better to contour features than to edges or bars, and about one-third exhibited systematic tuning for contour features. In particular, many cells were selective for contour feature orientation, responding to angles and curves pointing in a particular direction. There was a strong bias toward convex (as opposed to concave) features, implying a neural basis for the well-known perceptual dominance of convexity. Our results suggest that V4 processes information about contour features as a step toward complex shape recognition.