The invention discloses a preparation method of acid-sensitive degradation-controllable serial polymers with branched structures. The polymers are synthesized from ethylene glycol diglycidyl ether A and a diamine acid sensitive orthoester monomer B serving as frameworks, the molar ratio of A:B is 1-2:1, wherein the structural formulae is shown in the specification. Open loops of epoxy groups at both ends of A are polymerized with amino groups at both ends of B. When the molar ratio of A and B is 1:1, the polymers exist mainly in linear forms. With increase of molar ratio of A, the linear polymers are crosslinked (branched), so that net shapes are formed. When the molar ratio of A:B reaches 2:1, the polymers form three-dimensional netty structures. With increase of molar ratio of A: B, the branching degree of the polymers is improved. The polymers have cations and have the characteristics of acid sensitivity, degradation controllability and good biocompatibility, so that the polymers have important research value and application prospect in the field of gene therapy.