Recent observations have discovered a population of extended { Ly } \alpha sources , dubbed { Ly } \alpha blobs ( LABs ) , at high redshift z \sim 2 - 6.6 . These LABs typically have a luminosity of L \sim 10 ^ { 42 } -10 ^ { 44 } ~ { } { erg~ { } s ^ { -1 } } , and a size of tens of kiloparsecs , with some giant ones reaching up to D \sim 100 kpc . However , the origin of these LABs is not well understood . In this paper , we investigate a merger model for the formation of LABs by studying { Ly } \alpha emission from interacting galaxies at high redshifts by means of a combination of hydrodynamics simulations with three-dimensional radiative transfer calculations . Our galaxy simulations focus on a set of binary major mergers of galaxies with a mass range of 3 - 7 \times 10 ^ { 12 } ~ { } M _ { \odot } in the redshift range of z \sim 3 - 7 , and we use the newly improved ART ^ { 2 } code to perform the radiative transfer calculations which couple multi-wavelength continuum , ionization of hydrogen , and { Ly } \alpha line emission . We find that intense star formation and enhanced cooling induced by gravitational interaction produce strong { Ly } \alpha emission from these merging galaxies . The { Ly } \alpha emission appears to be extended due to the extended distribution of sources and gas . During the close encounter of galaxy progenitors when the star formation rate peaks at \sim 10 ^ { 3 } ~ { } { M _ { \odot } ~ { } yr ^ { -1 } } , our model produces LABs with luminosity of L \sim 10 ^ { 42 } -10 ^ { 44 } ~ { } { erg~ { } s ^ { -1 } } , and size of D \sim 10 - 20 ~ { } kpc at z > 6 and D \sim 20 - 50 kpc at z \sim 3 , in broad agreement with observations in the same redshift range . Our results suggest that merging galaxies may produce some typical LABs as observed , but the giant ones may be produced by mergers more massive than those in our model , or a combination of mergers and cold accretion from filaments on a large scale .