We proposed a new anisotropy function of kinetic coefficient for the phase-field simulations in two-dimension. The anisotropy function has minima at arbitrary polar angles. We carried out phase-field simulations of solidification of binary alloy with the new anisotropy function and found that the calculated growth form agreed with the kinetic Wulff shape, which is the exact solution determined by the anisotropy function. With the new anisotropy function, the kinetic Wulff shape is not necessary to be regular polygons but can be an arbitrary shape with any face angles. In addition, we introduced a curvature parameter with the aim of optimizing the anisotropy function. We found that the kinetic Wulff shape with flat facets was reproduced when the curvature parameter was at a standard value of about 20. The optimization based on the curvature parameter is applicable to other anisotropy functions. We concluded that our anisotropy function and the concept of the curvature parameter give us a great opportunity to simulate more general shapes of crystals. (C) 2013 Elsevier B.V. All rights reserved.