In this article, the meshless local Petrov-Galerkin (MLPG) method is applied to compute two steady-state heat conduction problems of irregular complex domain in 2D space. The essential boundary condition is enforced by the transformation method, and the MLS method is used for interpolation schemes. A numerical example that has analytical solution shows the present method can obtain desired accuracy and efficiency. Two cases in engineering with irregular boundary are computed to validate the approach by comparing the present method with the finite volume method (FVM) solutions obtained from a commercial CFD package FLUENT 6.3. The results show that the present method is in good agreement with FVM. It is expected that MLPG method (which is a truly meshless) is very promising in solving engineering heat conduction problems within irregular domains. (c) 2007 Published by Elsevier Ltd.