In this study, core structure dependent dislocation dynamics of a-type edge dislocation in three slip systems (basal, prismatic and pyramidal) of wurtzite GaN have been investigated using classical molecular dynamics simulations. All potential a-type edge dislocation cores in the shuffle and glide planes of the three slip systems have been identified, and the corresponding dislocation dynamics were examined. Our calculations reveal that for all of the three slip systems, all of the shuffle cores are planar glissile and mobile, while being non-planar sessile and immobile for all of the glide cores. We further show that vacancy can be used to activate the motion of glide cores via core transition from glide to shuffle, which is also valid for AlN and InN. The critical shear stresses for the motion of glide cores are also determined at various vacancy concentrations. Our study clarifies core structure dependent dislocation dynamics characteristics and provides ways in tuning dislocation motions in wurtzite crystals.