Online Social Media platforms (such as Twitter and Facebook) are extensively used for spreading the news to a wider public effortlessly at a rapid pace. However, now a days these platforms are also used with an aim of spreading rumors and fake news to a large audience in a short time span that can cause panic, fear, and financial loss to society. Thus, it is important to detect and control these rumors before it spreads to the masses. One way to control the spread of these rumors is by identifying possible suspicious users who are often involved in spreading the rumors. Our basic assumption is that the users who are often involved in spreading rumors are more likely to be suspicious in contrast to the users whose involvement in spreading rumors are less. This is due to the fact that sometimes, users may posts the rumor tweets by accident. In this paper, we use PHEME rumor tweet dataset which contains rumor and non-rumor tweets information on five incidents, that is, i) Charlie hebdo, ii)German wings crash, iii)Ottawa shooting, iv)Sydney siege, and v)Ferguson. We transform this rumor tweets dataset into suspicious users dataset before leveraging Graph Neural Network (GNN) based approach for identifying suspicious users. Specifically, we explore Graph Convolutional Network (GCN),which is a type of GNN, for identifying suspicious users and then we compare GCN results with the other three approaches which act as baseline approaches: SVM, RF and LSTM based deep learning architecture. Extensive experiments performed on real-world dataset, where we achieve up to 0.864 value for F1-Score and 0.720 value for AUC ROC, shows the effectiveness of GNN based approach for identifying suspicious users.