In the past decade, deep learning has been applied to various medical image analysis tasks. Skeletal bone age estimation is clinically important as it can help prevent age-related illness and pave the way for new anti-aging therapies. Recent research has applied deep learning techniques to the task of bone age assessment and achieved positive results. In this paper, we propose a bone age prediction method using a deep convolutional neural network. Specifically, we first train a classification model that automatically localizes the most discriminative region of an image and crops it from the original image. The regions of interest are then used as input for a regression model to estimate the age of the patient. The experiments are conducted on a whole-body scintigraphy dataset that was collected by Chonnam National University Hwasun Hospital. The experimental results illustrate the potential of our proposed method, which has a mean absolute error of 3.35 years. Our proposed framework can be used as a robust supporting tool for clinicians to prevent age-related diseases.