We introduce a surface streamline generation approach for visualizing vector fields defined on curved surfaces. This approach performs the intersection calculation on curved surface s with complex topology to achieve the highly detailed underlying vector. Then, an extended Runge -Kutta streamline integration technology is applied for performing streamline tracing on an unstructured mesh, where the adaptive stepsize strategy and intersection acceleration structure are presented for sake of simplicity and efficiency. Finally, this algorithm applies the ball feature to improve its visual intuitiveness and is integrated into the general visual analysis platform. Experimental results show that our method can generate continuous and consistent geometric surface streamlines by tracing streamlines on curved surfaces.