Neutron transport and energy composition of neutron beam extracted from a cylindrical discharge type fusion device was studied by using the computer simulation code, MCNP. In this study, three concepts of neutron beam optics (reflector and moderator) were proposed and examined; combined reflector which consists of two layers of different materials, inserting a moderator into the reflector to thermalize the neutron beam, and bending the extraction channel to avoid direct extraction of high energy neutrons. Combined reflector system produces 3.2 times higher neutron flux than no reflector when using W and Fe as outer and inner reflectors. The beam convergence is not dependent on reflector materials. Polyethylene (PE) and Fe combination produces fast neutron beam where more than 90% of the neutrons are fast. Combination of PE and D2O produces more than 30% thermalized neutron beam, but it contains epithermal and fast neutrons. When using moderator (D2O), the thickness of which is over 30 cm, more than 90% of the neutrons are thermalized. The bend angle of 20 degrees produces more than 80% thermalized neutron beam. Both inserting moderator and bending channel are effective to extract thermalized neutron beam. These results are useful for designing a neutron source which can produce specified neutron beam.