For a long time, steel has occupied the most of the market for transmission towers because of its high strength, stable performance and easy connection. In recent years, Fiber Reinforced Polymer (FRP) has become the focus of the power industry due to its advantages of high strength, light weight, corrosion resistance, easy processing and good insulation performance. Based on the overhead transmission line design specifications, design requirements, research and engineering practice experience, the structural design of the 35kV composite cross-arm tower is completed in the paper. The design of the cross-arm frame, the joint design and the dimensional design are considered. The finite element static analysis is carried out in ANSYS, and results show the maximum deflection of the cross-arm is 36.8mm in the condition of loads long-term effects. According to the national design code for overhead transmission lines, the maximum node displacement of the 35kV FRP cross-arm tower meets requirements of the national code. In addition, the maximum stress of the 35kV composite cross-arm tower is 242MPa, which is far less than the FRP strength values 1130MPa listed in the Mechanics of composite materials, so its design strength also meets the design requirements. Subsequently, through economic analysis, it shows that there are good economic benefits, social benefits and broad application prospects in the 35kV composite cross-arm tower.