A novel solving approach featuring bi-mapping, referred to as B-ICM, has been developed based on the ICM (independent, continuous, and mapping) method of structural topology optimization. B-ICM consists of two distinct steps: the first involves applying linear (L) mapping to the structural topology optimization problem, transforming it into a discrete model, and subsequently constructing the constraint function; the second entails implementing nonlinear (NL) mapping on this discrete model to create a continuous model, while converting continuous elemental topology variables into discrete ones. In contrast to the original ICM method, wherein the first step serves solely as a theoretical derivation, and the construction of constraint functions along with modeling and solving algorithms are all encompassed within the second step, which is categorized as a “one-step” approach, the B-ICM is classified as a “two-step” approach. Despite this distinction, it still employs the sequential dual quadratic programming algorithm commonly utilized in ICM methods for solving optimization models. We demonstrated this modeling and solving process using the structural topology optimization problem of volume minimization with displacement constraints. Results from both single-load and multi-load cases validated the effectiveness of our approach. We compared iteration count, clarity, and optimization capability across three methods for achieving distinct topologies: (1) the SIMP method considering Heaviside projection, (2) the floating projection topology optimization (FPTO) method, (3) the non-penalized method of smooth-edged material distribution for optimizing topology (SEMDOT), as well as the original ICM method. Results indicated that B-ICM outperforms these alternatives. This study not only enhances the modeling strategy and refines the solution approach of the ICM method, but also offers a superior technique for addressing blurry boundary problems. In continuum topology optimization, optimal topologies with blurry boundaries are typically generated through filtering operations designed to mitigate checkerboard patterns and mesh dependency issues. Notably, an increase in the filtering radius results in a more blurred boundary. Our study successfully addressed this challenge by achieving clear boundaries for optimal topologies. Importantly, the key techniques developed here are applicable to all continuous variable optimization methods, including the variable density method.