The continuous emergence of new targets in open scenarios leads to a substantial decrease in the performance of Inverse Synthetic Aperture Radar (ISAR) recognition systems. Also, data scarcity further exacerbates the challenge of identifying new classes of ISAR targets. In this paper, a few-shot incremental target recognition framework based on Scattering-Topology Properties (STPIL) is proposed. Specifically, STPIL extracts scattering-topology properties of ISAR targets as recognition features. Meanwhile, the pseudo-incremental training strategy effectively alleviates the algorithm’s forgetting of old knowledge, and improves compatibility with new classes. Besides, a feature embedding network, with few parameters, is designed based on the graph neural network. This embedding network is highly adaptable to changes in data distribution. Additionally, STPIL fully considers the joint distribution and marginal distribution in scattering features, and uses the Brownian distance metric module to make the scattering-topology features more discriminative. Experimental results on both the simulation dataset and the public measured data indicate that STPIL can effectively balance new classes with old classes, and has superior performance to other advanced methods in the incremental recognition of targets.