In boundary detection of color images, it is essential to form local edge elements that are detected by a local edge detection method into groups for finding straight or curved lines. A new boundary detection method based on the Hopfield neural network is proposed. First, an image is divided into blocks. In each block, two edge segments at the most are detected. Then, a unit of the network is assigned to each edge segment. Some properties of edge segments belonging to a boundary are embedded in an objective function of the network, and the boundary is detected by minimizing the function. Experimental results show that the method is applicable for partially disconnected and/or blurred boundaries.