In recent years, many researchers have shown increasing interest in music information retrieval (MIR) applications, with automatic chord recognition being one of the popular tasks. Many studies have achieved/demonstrated considerable improvement using deep learning based models in automatic chord recognition problems. However, most of the existing models have focused on simple chord recognition, which classifies the root note with the major, minor, and seventh chords. Furthermore, in learning-based recognition, it is critical to collect high-quality and large amounts of training data to achieve the desired performance. In this paper, we present a multi-task learning (MTL) model for a guitar chord recognition task, where the model is trained using a relatively large-vocabulary guitar chord dataset. To solve data scarcity issues, a physical data augmentation method that directly records the chord dataset from a robotic performer is employed. Deep learning based MTL is proposed to improve the performance of automatic chord recognition with the proposed physical data augmentation dataset. The proposed MTL model is compared with four baseline models and its corresponding single-task learning model using two types of datasets, including a human dataset and a human combined with the augmented dataset. The proposed methods outperform the baseline models, and the results show that most scores of the proposed multi-task learning model are better than those of the corresponding single-task learning model. The experimental results demonstrate that physical data augmentation is an effective method for increasing the dataset size for guitar chord recognition tasks.