The meshless local Petrov-Galerkin scaled boundary method (MLPG-SBM) is developed for analyzing steady heat conduction problems in this paper. As a boundary-type meshless method, the MLPG-SBM only requires a meshless local Petrov-Galerkin discretization in the circumferential direction and seeks analytical solutions in the radial direction. Higher accuracy and faster convergence are obtained due to the increased smoothness and continuity of the shape functions. Based on the MLPG-SBM, the steady heat conduction problems with thermal singularity and unbounded domain can be ideally modeled. Some numerical examples are presented to validate the availability and accuracy of the present method for steady heat conduction analysis.