This paper is about fully-distributed support vector machine (SVM) learning over wireless sensor networks. With the concept of the geometric SVM, we propose to gossip the set of extreme points of the convex hull of local data set with neighboring nodes. It has the advantages of a simple communication mechanism and finite-time convergence to a common global solution. Furthermore, we analyze the scalability with respect to the amount of exchanged information and convergence time, with a specific emphasis on the small-world phenomenon. First, with the proposed naive convex hull algorithm, the message length remains bounded as the number of nodes increases. Second, by utilizing a small-world network, we have an opportunity to drastically improve the convergence performance with only a small increase in power consumption. These properties offer a great advantage when dealing with a large-scale network. Simulation and experimental results support the feasibility and effectiveness of the proposed gossip-based process and the analysis.