A multifocal metalens, which focuses incident light at multiple foci, has many applications in imaging systems and optical communications. However, the traditional design strategy of a multifocal metalens combines several lenses that have different focal points into a planar integrated unit, resulting in low imaging quality because of the high background noise. Here we show that the defects of the traditional method can be overcome by designing a metalens with conic shapes (the ellipse and the hyperbola); this approach could improve the imaging performance and substantially decrease the background noise of multifocal metalenses. These benefits arise from the intrinsic properties of the two conic curves, which can focus incident light constructively at all of the foci of the metalens. We further demonstrate that the proposed conic-shaped metalens can function well within a broadband operation wavelength that ranges from 600 to 900 nm with the dual polarity actively controlled by the incident circular polarized light. The great agreement between the experimental and simulation results demonstrates that our proposed metalens has significant potential for use in future integrated nanophotonic devices.