Lie symmetry theory is an effective method to find exact solution of mathematical and physical equations. The symmetry and reduced equations of Brinkman model are derived based on Lie symmetry theory. Some new exact solutions of the equation are obtained by solving the reduced equations, including variable separation and traveling wave solutions. Some variable separation solutions contain the effect of anisotropy of thermal conductivity on temperature. These solutions and traveling wave solutions are not reported in the existent literature, and they can more realistically reflect the natural convection flow in Brinkman model.