The scaled boundary finite element method (SBFEM) combined with isogeometric analysis (IGA) is proposed to solve the two-dimensional steady-state heat conduction problems in complex geometries. The main benefit of SBFEM is that the spatial dimension of analyzed domain is reduced by one and the solution is analytical in the radial direction. In this method, only the boundary of the computational domain requires discretization with finite elements leading to the reduction of computational efforts. However, SBFEM suffers from the finite element method related drawbacks. In the case of the complex geometric shapes, a large number of elements are necessary to obtain the exact representation of geometry in finite element method. Isogeometric analysis is a novel numerical technique based on the non-uniform rational B-splines (NURBS), where the geometry can be exactly represented. Moreover, this technique yields superior numerical accuracy, efficiency and convergence property in comparison to finite element method. In the proposed method, the segments of domain boundary with complex geometries are described with NURBS basis functions in IGA, while the straight segments of boundary are represented with polynomial basis functions as in the conventional SBFEM. Thus, the present approach combines the advantages of both SBFEM and IGA. The heat conduction problems of complex geometry can be more effectively handled with the proposed method considering the prescribed heat fluxes and temperatures on side-faces. The accuracy and efficiency of the proposed formulation are demonstrated by modeling five numerical examples involving the complicated geometry. (C) 2017 Elsevier Ltd. All rights reserved.