Machine learning, particularly deep neural networks, has been widely utilized in high energy physics and has shown remarkable results in various applications. Moreover, the concept of machine learning has been extended to quantum computers, giving rise to a new research area known as quantum machine learning. In this paper, we propose a novel variational quantum circuit model, Quantum Complete Graph Neural Network (QCGNN), designed for learning complete graphs. We argue that QCGNN has a polynomial speedup against its classical counterpart, due to the property of quantum parallelism. In this paper, we study the application of QCGNN through the challenging jet discrimination, where the jets are represented with complete graphs. Subsequently, we conduct a comparative analysis with classical graph neural networks to establish a benchmark.