We　use　the　approach　of　＂transitionless　quantum　driving＂　proposed　by　Berry　to　construct　shortcuts　to　the　population　transfer　and　the　creation　of　maximal　entanglement　between　two　A-type　atoms　based　on　the　cavity　quantum　electronic　dynamics　system.　An　effective　Hamiltonian　is　designed　by　resorting　to　an　auxiliary　excited　level,　a　classical　driving　field,　and　an　extra　cavity　field　mode　to　supplement　or　substitute　the　original　reference　Hamiltonian,　and　steer　the　system　evolution　along　its　instantaneous　eigenstates　in　an　arbitrarily　short　time,　speeding　up　the　rate　of　population　transfer　and　creation　of　maximal　entanglement　between　the　two　atoms　inside　a　cavity.　Numerical　simulation　demonstrates　that　our　shortcuts　are　robust　against　the　decoherences　caused　by　atomic　spontaneous　emission　and　cavity　photon　leakage.