In order to study the regulation of terahertz wave transmission characteristics by subwavelength structure of surface modified cosine grooves, a terahertz sub-wavelength metal Cu slit structure is proposed and the transmission spectrum characteristics of terahertz wave are simulated based on finite-difference time-domain method. The simulation results show that the transmission intensity and phase characteristics of terahertz waves can be controlled by changing the structure configuration, number, period and depth of the cosine grooving on the upper and lower surfaces of metal Cu slit structure.