Summary: In order to efficiently retrieve, analyze, store and transmit large amount of vector data, it is extremely necessary to compress these vector data in advance. Based on elegant properties of the B-spline (e.g., locality and smoothness), we propose a cubic B-spline-based algorithm to compress the vector data with boundary constraints. The proposed cubic B-spline vector data compression algorithm is tested on nine examples with curve vector data. We also compare numerical results produced by the proposed algorithm with these of the classical Douglas-Peucker compression algorithm. Numerical results show that the proposed cubic B-spline-based vector compression algorithm not only can significantly reduce the compression rate, but also can produce highly accurate compression curve with \({C^2}\)-smoothness. Therefore, the algorithm has many important potential applications (e.g., automatic drive).