We　propose　a　method　to　entangle　two　vibrating　microsize　mirrors　(i.e.,　mechanical　oscillators)　in　a　cavity　optomechanical　system.　In　this　scheme,　we　discuss　both　the　resonant　and　large-detuning　conditions,　and　show　that　the　entanglement　of　two　mechanical　oscillators　can　be　achieved　with　the　assistance　of　a　two-level　atom　and　cavity-radiation　pressure.　In　the　resonant　case,　the　operation　time　is　relatively　short,　which　is　desirable　to　minimize　the　effects　of　decoherence.　While　in　the　large-detuning　case,　the　cavity　is　only　virtually　excited　during　the　interaction.　Therefore,　the　decay　of　the　cavity　is　effectively　suppressed,　which　makes　the　efficient　decoherence　time　of　the　cavity　to　be　greatly　prolonged.　Thus,　we　observe　that　this　virtual-photon　process　of　microscopic　objects　may　induce　the　entanglement　of　macroscopic　objects.　Moreover,　in　both　cases,　the　generation　of　entanglement　is　deterministic　and　no　measurements　on　the　atom　and　the　cavity　are　required.　These　are　experimentally　important.　Finally,　the　decoherence　effect　and　the　experimental　feasibility　of　the　proposal　are　briefly　discussed.　©　2018,　Higher　Education　Press　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.