The Lyman-alpha line at 121.6 nm emitted by hydrogen, the most abundant element of the sun, plays a fundamental role in solar and coronal physics. As an intense chromospheres line, it is used to analyze many chromospheres features. To observe the Lyman alpha radiations in the field of 1.1R⊙ to 2.5R⊙ (R⊙ is solar radius), a reflective Lyman-alpha coronagraph with an aperture 40 mm, focal length 590 mm is designed. Two aspheric surfaces and one spherical mirror are adopted, and one piece of reflective mirror is used to fold the light path. The system′s transfer function is close to the diffraction limit, and the main stray light could be suppressed under 10-6 of solar photosphere radiation, which is in an acceptable level of the Lyman-alpha corona measurement.