Ly-alpha emitting galaxies and giant Ly-alpha blobs (LABs) have been extensively observed to study the formation history of galaxies. However, the origin of their extended Ly-alpha emission, especially of LABs, remains controversial. Polarization signals from some LABs have been discovered, and this is commonly interpreted as strong evidence supporting that the extended Ly-alpha emission originates from the resonance scattering. The Monte Carlo Ly-alpha radiative transfer code LaRT is updated to investigate the polarization of Ly-alpha using the Stokes vector formalism. We apply LaRT to a few models to explore the fundamental polarization properties of Ly-alpha. Interestingly, individual Ly-alpha photon packets are found to be almost completely polarized by a sufficient number of scatterings (N_scatt > 10^4-10^5 in a static medium) or Doppler shifts induced by gas motion, even starting from unpolarized light. It is also found that the polarization pattern can exhibit a non-monotonically increasing pattern in some cases, besides the commonly-known trend that the polarization monotonically increases with radius. The polarization properties are primarily determined by the degree of polarization of individual photon packets and the anisotropy of the Ly-alpha radiation field, which are eventually controlled by the medium's optical depth and velocity field. If once Ly-alpha photon packets achieve ~100% polarization, the radial profile of polarization appears to correlate with the surface brightness profile. A steep surface brightness profile tends to yield a rapid increase of the linear polarization near the Ly-alpha source location. In contrast, a shallow surface brightness profile gives rise to a slowly increasing polarization pattern.