variavel0=Fábio Alencar Schneider - eng_schneider@yahoo.com.br UFSC Clovis Raimundo Maliska - maliska@sinmec.ufsc.br UFSC Abstract. This work presents a numerical method for the solution of the convection/diffusion equation for a scalar variable, using the Finite Volume Method in unstructured grids. These grids have better adaptive ness for simple and complex domains, allowing that local refinement in specific regions. The employed mesh and the construction of the control volumes are based on the element discretization, what it facilitates the computational implementation. The formulation is presented in the basic form. The presented method is compared with other numerical methods that use unstructured grids. Keywords. numerical method, unstructured grids, fluid flow.