Federated　learning　(FL)　provides　a　learning　framework　without　participants　sharing　local　raw　data,　but　individual　privacy　is　still　at　risk　of　disclosure　through　attacking　the　trained　models.　Due　to　the　strong　privacy　guarantee,　differential　privacy　(DP)　is　widely　applied　to　FL　to　avoid　privacy　leakage.　Traditional　private　learning　adds　noise　directly　to　the　gradients.　The　continuous　accumulated　noise　on　parameter　models　severely　impairs　learning　effectiveness.　To　solve　this　problem,　we　introduce　the　idea　of　differentially　private　continuous　data　release　(DPCR)　into　FL　and　propose　an　FL　framework　based　on　DPCR　(FL-DPCR).　Meanwhile,　our　proposed　Equivalent　Aggregation　Theorem　demonstrates　that　DPCR　effectively　reduces　the　overall　error　added　to　parameter　models　and　improves　FL＇s　accuracy.　To　improve　FL-DPCR＇s　learning　effectiveness,　we　introduce　Matrix　Mechanism　to　construct　a　release　strategy　and　design　a　binary-indexed-tree　(BIT)　based　DPCR　model　for　Gaussian　mechanism　(BCRG).　By　solving　a　complex　nonlinear　programming　problem　with　negative　exponents,　BCRG　achieves　optimal　release　accuracy　efficiently.　Besides,　we　exploit　the　residual　privacy　budget　to　boost　the　accuracy　further　and　propose　an　advanced　BCRG　version　(ABCRG).　Our　experiments　show　that,　compared　to　traditional　FL　with　DP,　our　achievements　improve　the　accuracy　with　gains　ranging　from　$3.4\%$　on　FMNIST　to　$65.7\%$　on　PAMAP2.　IEEE