The simulation of paper marbling through computers can help designers create unique, novel, and artistic paper marbling image patterns, which is important for the protection, record, and inheritance of this kind of ancient art. However, related techniques have not been researched intensively. In this paper, a new paper marbling method based on the techniques of fluid dynamics vector graphics is proposed. The method is fast and stable, and achieves clear silhouettes of the pattern boundaries. First, a semi-Lagrange method to solve the fluid equation and obtain the velocities of two-dimensional incompressible fluid field is used. Considering vector graphics has the advantage that can not be affected by the resolution, the study tracks the movement of the fluid boundary to generate the outline of the marbling image. Then, the paper renders the outline by the stencil method and exports the shape as the Scalable Vector Graphics (SVG) image. Moreover, the above method is extended for simulation of paper marbling generated with multiple dyes, which can generate more colorful marbling patterns. In addition, the study combines the method with the mathematical transform method to simulate marbling shapes with special patterns.