This paper presents the Lucas polynomial solution of second-order nonlinear ordinary differential equations with mixed conditions. Lucas matrix method is based on collocation points together with truncated Lucas series. The main advantage of the method is that it has a simple structure to deal with the nonlinear algebraic system obtained from matrix relations. The method is applied to four problems. In the first two problems, exact solutions are obtained. The last two problems, Bratu and Duffing equations are solved numerically; the results are compared with the exact solutions and some other numerical solutions. It is observed that the application of the method results in either the exact or accurate numerical solutions.