<p>The isogeometric analysis (IGA) framework, which employs non-uniform rational B-splines (NURBS) basis functions, provides a seamless integration between computer-aided design (CAD) and finite element analysis (FEA) through the utilization of a common mathematical representation for both design and analysis. This unified paradigm has demonstrated substantial efficacy in structural topology optimization applications. In this study, we propose a nonlinear isogeometric level-set method for topology optimization of continuum structures, integrating the level-set method with IGA to establish a unified framework. The primary innovation lies in the use of a single NURBS mesh for simultaneously solving the level-set equation, reinitialization equation, and elasticity problems. The weak form formulations of the level-set and reinitialization equations are derived within the isogeometric context, yielding nonlinear isogeometric level-set finite element equations. Furthermore, isogeometric linearized incremental equations are formulated based on the level-set function increment, facilitating the propagation of material interfaces. The shape derivative governing this propagation is computed from the element strain energy distributed across the NURBS mesh. The proposed method efficiently handles complex topological changes, such as the merging and splitting of material regions, on curved and multi-patch NURBS meshes, while ensuring smooth boundary evolution. To validate the proposed method, several numerical examples are presented, including interface propagation, reinitialization, and topology optimization. These examples highlight the method's effectiveness and robustness, particularly in topology optimization that involves intricate geometries. The results underscore the method's capability to generate high-quality solutions for complex geometries, solidifying its potential in advanced topology optimization applications.</p>