There are many studies on face recognition, which identifies a person using distinctive features extracted from a face image. One of the problems in face recognition is that the accuracy of face recognition decreases due to environmental changes such as head pose, emotion, illumination, etc. Addressing this problem, soft biometrics, which uses attributes such as age and gender for person authentication, is expected to improve the accuracy of face recognition. This paper proposes a face attribute estimation method using the Convolutional Neural Network (CNN). The CNN architecture of the proposed method, called DendroNet, is automatically designed according to the relationships among attributes. Though experiments using the CelebA dataset, we demonstrate that the proposed method exhibits better performance than conventional methods.