This paper presents a new Android malware detection method based on Graph Neural Networks (GNNs) with Jumping-Knowledge (JK). Android function call graphs (FCGs) consist of a set of program functions and their inter-procedural calls. Thus, this paper proposes a GNN-based method for Android malware detection by capturing meaningful intra-procedural call path patterns. In addition, a Jumping-Knowledge technique is applied to minimize the effect of the over-smoothing problem, which is common in GNNs. The proposed method has been extensively evaluated using two benchmark datasets. The results demonstrate the superiority of our approach compared to state-of-the-art approaches in terms of key classification metrics, which demonstrates the potential of GNNs in Android malware detection and classification.