We propose a transmission-filter coronagraph for direct imaging of Jupiter-like exoplanets with ground-based telescopes. The coronagraph is based on a transmission filter that consists of finite number of transmission steps. A discrete optimization algorithm is proposed for the design of the transmission filter that is optimized for ground-based telescopes with central obstructions and spider structures.We discussed the algorithm that is applied for our coronagraph design. To demonstrate the performance of the coronagraph, a filter was manufactured and laboratory tests were conducted. The test results show that the coronagraph can achieve a high contrast of 10 to -6.5 at an inner working angle of 5{\lambda}/D, which indicates that our coronagraph can be immediately used for the direct imaging of Jupiter-like exoplanets with ground-based telescopes.