The Galactic high-mass X-ray binary and jet source ( microquasar ) LSI +61 303 has recently been detected at TeV \gamma -ray energies by the MAGIC telescope . We have applied a time-dependent leptonic jet model to the broadband spectral energy distribution and suggested ( though not unambiguously detected ) orbital modulation of the very high energy \gamma -ray emission of this source . Our model takes into account time dependent electron injection and acceleration , and the adiabatic and radiative cooling of non-thermal electrons . It includes synchrotron , synchrotron self-Compton and external inverse Compton ( with seed photons from the companion star ) , as well as \gamma \gamma absorption of \gamma -rays by starlight photons . The model can successfully reproduce the available multiwavelength observational data . Our best fit to the SED indicates that a magnetic field of B _ { 0 } \sim 5 \times 10 ^ { 3 } G at \sim 10 ^ { 3 } R _ { g } is required , and electrons need to be accelerated out to TeV energies ( \gamma _ { 2 } = 10 ^ { 6 } ) with a nonthermal injection spectrum with a spectral index of q = 1.7 , indicating the operation of acceleration mechanisms beyond the standard first-order Fermi mechanism at relativistic or non-relativistic shocks . The orbital modulation of the VHE \gamma -ray emission can be explained solely by the geometrical effect of changes in the relative orientation of the stellar companion with respect to the compact object and jet as it impacts the position and depth of the \gamma \gamma absorption trough . Such a scenario predicts a trend of spectral hardening during VHE \gamma -ray low orbital phases .