Summary: Higher-order panel methods are used to solve the Laplace equation in the presence of complex geometries. These methods are useful when globally accurate velocity or potential fields are desired as in the case of vortex-based fluid flow solvers. This paper develops a fast multipole algorithm to compute velocity fields due to higher-order, two-dimensional vortex panels. The technique is applied to panels having a cubic geometry and a linear distribution of vorticity. The results of the present method are compared with other available techniques.