  LS I +61$^\circ$ ~303 is one of around ten gamma-ray binaries detected so far
which has a spectral energy distribution dominated by MeV-GeV photons. It is
located at a distance of 2 kpc and consists of a compact object (black hole or
neutron star) in an eccentric orbit around a 10-15 $M_{\odot}$ Be star, with an
orbital period of 26.496 days. The binary orbit modulates the emission ranging
from radio to TeV energies. A second, longer, modulation period of 1667 days
(the super-orbital period) has also been detected from radio to TeV
observations. The VERITAS imaging atmospheric Cherenkov telescope array has
been observing LS I +61$^\circ$ ~303 since 2006, and has accumulated a dataset
that fully covers the entire orbit. Increased coverage of the source in the
very-high-energy band is currently underway to provide more results on the
modulation pattern, super-orbital period, and orbit-to-orbit variability at the
highest energies. The spectral measurements at the highest energies will reveal
more information about gamma-ray production/absorption mechanisms, the nature
of the compact object, and the particle acceleration mechanism. Using >150 hrs
of VERITAS data, we present a detailed study of the spectral energy
distribution and periodic behavior of this rare gamma-ray source type at
very-high energy.
