Commutative encryption and watermarking (CEW) is an emerging method that combines encryption technology with digital watermarking technology. It has the dual capability of secure transmission and copyright protection. However, the existing CEW methods for vector maps have good robustness in resisting geometric attacks but poor resistance to vertex attacks (e.g., addition, deletion, etc.). To solve this problem, here we propose a novel invariant-based CEW algorithm for vector maps, which consists of permutation-based encryption scheme and coordinates-based watermarking scheme. In the encryption scheme, the encryption key is generated via the Gaussian distribution method combined with the SHA-512 hash method; then, the double random position permutation strategy is applied to the vector map encryption. In watermarking embedding scheme, the original watermark image is scrambled via logistic chaotic encryption before embedding, and the coordinates of all the vertices are normalized. Then, the scrambled watermark image is embedded into the normalized coordinates. Results show that: proposed method is more robust to conventional attacks (e.g., vertex addition and deletion, reordering and data format conversion) and geometric attacks (e.g., scaling and translation). In addition, compared with the existing CEW methods for vector maps, the proposed method has higher security and stronger robustness against vertex attacks.