The modeling of a spiral bevel gear (SBG) is a fundamental work to its design, analysis and manufacturing. The essential work of modeling SBGs is the generation of tooth surface points that meet the strict accuracy requirement of the SBG industry. Specially, if those points are evenly distributed, the 3D models can be efficiently generated by developing automatic programs, or else the tedious manual modeling process are usually applied with 3D commercial software. Hence, it is very beneficial to accurately generating those evenly distributed points with an approach that can stably and efficiently solve the highly nonlinear equations related to the complicated tooth surface geometry. This work proposed such an approach to the SBG produced by face-milled generated (FMG) method. First, two representations of the geometric meshing theory (GMT) are introduced to calculate tooth surfaces of different cases as closed-form (explicit) results rather than implicit results. Subsequently, a new strategy is employed to accurately and efficiently obtain the tooth surface points that are approximately even-distributed. Furthermore, an advanced geometric iterative optimization algorithm (GIOA) is developed to solve the nonlinear equations in a stable way. With the calculated tooth surface points, a special automatic program is developed to accomplish the 3D modeling of SBGs. Examples are discussed to show the validity of this work.