We　construct　shortcuts　to　adiabatic　passage　to　achieve　controllable　and　fast　quantum-information　transfer　(QIT)　between　arbitrary　two　distant　nodes　in　a　two-dimensional　(2D)　quantum　network.　Through　suitable　designing　of　time-dependent　Rabi　frequencies,　we　show　that　perfect　QIT　between　arbitrary　two　distant　nodes　can　be　rapidly　achieved.　Numerical　simulations　demonstrate　that　the　proposal　is　robust　to　the　decoherence　caused　by　atomic　spontaneous　emission　and　cavity　photon　leakage.　Additionally,　the　proposed　scheme　is　also　insensitive　to　the　variations　of　the　experimental　parameters.　Thus,　the　proposed　scheme　provides　a　new　perspective　on　robust　quantum　information　processing　in　2D　quantum　networks.