Abstract: This paper describes an adaptive and efficient algorithm for polygonization of implicit surfaces.The algorithm covers two steps:initial polygonization and adaptive refinement.In the first step, an initial coarse triangular mesh is created from the implicit surface using a variation of the traditional Marching Cubes Algorithm.And then in the second step,the triangles in the coarse mesh are recursively subdivided by employing a sampling rate that varies spatially according to local complexity of the surface.The vertices newly created in the refined mesh are projected onto the implicit surface by gradientdescending method.Consequently,the algorithm produces the minimum number of polygons required to approximate the surface with a desired precision and the final mesh is simplicial complex.Our algorithm can be used in the real-time environment of visualization to implicit surfaces.