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With the tremendous expansion of graphs data, node classification shows its great importance in many real-world applications. Existing graph neural network based methods mainly focus on classifying unlabeled nodes within fixed classes with abundant labeling. However, in many practical scenarios, graph evolves with emergence of new nodes and edges. Novel classes appear incrementally along with few labeling due to its newly emergence or lack of exploration. In this paper, we focus on this challenging but practical graph few-shot class-incremental learning (GFSCIL) problem and propose a novel method called Geometer. Instead of replacing and retraining the fully connected neural network classifer, Geometer predicts the label of a node by finding the nearest class prototype. Prototype is a vector representing a class in the metric space. With the pop-up of novel classes, Geometer learns and adjusts the attention-based prototypes by observing the geometric proximity, uniformity and separability. Teacher-student knowledge distillation and biased sampling are further introduced to mitigate catastrophic forgetting and unbalanced labeling problem respectively. Experimental results on four public datasets demonstrate that Geometer achieves a substantial improvement of 9.46% to 27.60% over state-of-the-art methods.