The invention discloses a topology optimization method for isotropic materials based on second-order cone programming. The method takes Young's modulus E and Poisson's ratio v of isotropic materials as design variables, and performs singular value decomposition on the unit stiffness matrix. Construct a new decomposition representation of the stiffness matrix; and map the original design variables (E,v) to a new set of design variables (P,Q) through a bijective function, take (P,Q) as the design variables, and convert the original The topology optimization problem is transformed into a second-order cone programming problem, so as to obtain the global optimal (P, Q) solution, and obtain the corresponding optimal Young's modulus and Poisson's ratio through the bijective function; for any given target material category, the continuous solution is hierarchically clustered in (P,Q) space to obtain a high-fidelity discrete solution. By transforming the topology optimization problem of free isotropic materials into a second-order cone programming problem, the method of the invention can theoretically ensure the optimal solution of the problem and can obtain high-fidelity discrete solutions under any specified number of materials.