In a solar coronagraph, the most important component is an occulter to block the direct light from the disk of the sun. Because the intensity of the solar outer corona is 10−6 to 10−10 times of that of the solar disk (I⊙), it is necessary to minimize scattering at the optical elements and diffraction at the occulter. Using a Fourier optic simulation and a stray light test, we investigated the performance of a compact coronagraph that uses an external truncated-cone occulter without an internal occulter and Lyot stop. In the simulation, the diffracted light was minimized to the order of 7.6 × 10−10 I⊙ when the cone angle c was about 0.39◦. The performance of the cone occulter was then tested by experiment. The level of the diffracted light reached the order of 6 × 10−9 I⊙ at c = 0.40◦. This is sufficient to observe the outer corona without additional optical elements such as a Lyot stop or inner occulter. We also found the manufacturing tolerance of the cone angle to be 0.05◦, the lateral alignment tolerance was 45 μm, and the angular alignment tolerance was 0.043◦. Our results suggest that the physical size of coronagraphs can be shortened significantly by using a cone occulter.