The impacts of polarization mode dispersion (PMD) on the pulse width in linear systems have been investigated. The analytical solutions, including the effects of initial frequency chirp, are derived. The results show that the broadening effects induced by the first order PMD are independent on group velocity dispersion (GVD) and chirp, which are different from the effects induced by the second order PMD. An initially chirped Gaussian pulse is taken as an example. Analytical solutions of rms pulse width are obtained before and after first order PMD compensation. It is shown that the broadening effects will be suppressed effectively by appropriately choosing GVD and chirp parameter; the post transmission compensation method will be less efficient than the PSP transmission method due to chirp.