Abstract: The analytical expression of Jones matrix for second-order PMD of a single-mode fiber has been derived from the relation between PMD vector and Jones matrix.This matrix could be used to determine the output temporal pulse expression in a second-order PMD approximation and it is applied to simulate the impact of PMD on the quality of signal transmission.It shows that the signal will become bad with the increase of transmission velocity and distance by comparing the wave figure and eye diagram of input and output pulse. Furthermore, the influence of the second-order PMD must be considered when the rotation velocity of principal states of polarization(PSP) increases. Above results can be used to design fiber-optic communication systems when the impact of PMD needs to be considered.