The singularities,oscillatory performances and the contributing factors to the 3-D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part,are analyzed systematically.Relative numerical integral methods about the two parts are presented in this paper.An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function,which makes the improvement of calculation efficiency and accuracy possible.And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function.Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance.Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.