With a large number of sensors and control units in networked systems, distributed support vector machines (DSVMs) play a fundamental role in scalable and efficient multi-sensor classification and prediction tasks. However, DSVMs are vulnerable to adversaries who can modify and generate data to deceive the system to misclassification and misprediction. This work aims to design defense strategies for DSVM learner against a potential adversary. We use a game-theoretic framework to capture the conflicting interests between the DSVM learner and the attacker. The Nash equilibrium of the game allows predicting the outcome of learning algorithms in adversarial environments, and enhancing the resilience of the machine learning through dynamic distributed algorithms. We develop a secure and resilient DSVM algorithm with rejection method, and show its resiliency against adversary with numerical experiments.