In this paper, a 3D thermal LB model on non-orthogonal grid is derived, as well as the corresponding boundary treatment method for irregular boundary. Numerical validation is then performed by modeling natural convection in a 3D annulus. It is proved that the thermal flow structure in the annulus is accurately predicted with less grids. After that, present method is applied to study natural convection in a 3D cavity with inclined side walls. Two opposite inclined walls on the left and right sides are kept at different constant temperatures, while the remained four walls of the cavity are either adiabatic (Type 1) or own linear temperature variations (Type 2). It is found out that natural convection in the inclined cavity exhibits distinct 3D features under Type 2 thermal boundary setting, yet it can be viewed as a 2D process under Type 1 condition. Moreover, a large Prandtl number (Pr = 10.0) can generally suppress the 3D effect stemmed from thermal boundary setting. The aforementioned results indicate that present model and boundary treatment method are reliable to deal with 3D natural convection in irregular domains. (C) 2019 Elsevier Ltd. All rights reserved.