This paper presents the flow analysis of flow over a cylindrical helical-blade turbine to investigate its optimum performance by varying design parameters. For numerical investigations, shear stress transport (SST) turbulence model is used. This simulation is carried out using commercial code CFX by ANSYS Inc. In this paper, the shape optimization was of turbine blades with NACA0021 performed for the vertical-axis turbine having the cylindrical shape. The influences of blade angle of attack, helical angle, and solidity on each shape are grasped. From of the flow analysis, power coefficient decreased when the helical angle was 20 degrees or more, and no electricity is produced when the solidity of 0.1. As a result of the shape optimization, the cylindrical turbine showed the highest power coefficient of 0.2733 at 3° of the blade angle of attack, 10° of the helical angle, and 0.2 of the solidity at the tip speed ratio of 1.