Organizations　tend　to　collaboratively　train　the　deep　learning　model　over　their　combined　datasets　for　a　common　benefit　(e.g.,　better-trained　model　or　learning　a　complicated　model).　However,　due　to　the　consideration　about　privacy　leakage,　organizations　cannot　share　their　data　directly,　especially　related　to　sensitive　domains.　In　this　article,　a　privacy-preserving　collaborative　deep　learning　mechanism,　namely　Sigma,　is　designed　to　allow　participating　organizations　to　train　a　collective　model　without　exposing　their　local　training　data　to　the　others.　Specifically,　a　single-server-aided　private　collaborative　architecture　is　introduced　to　achieve　the　private　collaborative　learning,　which　protects　organizations＇　data　even　if　n　-　1　out　of　n　participants　colluded.　We　also　design　a　practical　protocol　to　perform　the　secure　model　training,　which　can　resist　the　typical　inference　attack　through　the　sharing　information.　After　that,　we　propose　a　fair　model　releasing　mechanism　for　participants　and　introduce　differential　privacy　to　prevent　model　stealing　and　membership　inference　attack.　Furthermore,　we　prove　that　Sigma　can　ensure　participants＇　privacy　preservation　and　analyze　the　communication　overhead　in　theory.　To　evaluate　the　effectiveness　and　efficiency　of　Sigma,　we　conduct　an　experiment　over　two　real-world　datasets　and　the　simulation　results　demonstrate　that　Sigma　can　efficiently　achieve　the　collaborative　model　training　and　effectively　resist　the　membership　inference　attack.