It is important to improve the precision of the reconstructed surfaces from volume data. The marching cubes method and its precision are analyzed in detail. It is found that the error brought by the marching cubes method can reach to 1.5 pixels, which is a serious problem for reconstructing the small and thin objects, such as human blood vessels. A new method with more precision is presented. The new method distinguishes the pixels inside, across or outside of the boundary by a threshold, and determines the position of the boundary point according to the values of the three adjacent pixels (inside, across and outside), which is different from the marching cubes. The new method also modifies the grid topology of the MC method, considering the position change of boundary points. Theoretical analysis shows that the new method can find the accurate boundary points when the boundary is a straight line in a pixel. The precision and overhead of the new method are discussed. Finally examples of CT data show the contrast between the new method and the MC method.