The down-ground oscillatory focus has dynamic effects on the ground,it is important to study these responses for earthquake disaster reduction,shockproof,inversion of the oscillatory focus and so on. In this paper,the dynamic response problem of the out-of-plane harmonic circular oscillatory focus in the half-space was studied,at first,imaginary focus was used to give the displacement wave functions which can satisfy the stress-free boundary of the half-space,and the stress conditions on the boundary of the circular oscillatory focus was utilized to obtain the non-linear equation of the unknown coefficients,and the Graf addition formula and Fourier series expansion were used to obtain an infinite linear equations,and was solved with the finite truncation method with enough computation precision,at last,the displacement and the stress in the media can be obtained. The variations of the ground displacement and the tangential shearing stress around the boundary of the circular oscillatory focus were discussed by a given example,and the results showed the effectiveness.