In　this　paper　we　consider　approximating　smooth　solutions　of　systems　of　nonlinear　conservation　laws　by　a　linear　finite　element　method　with　uniform　mesh　in　two　spatial　dimensions,　where　the　time　discretization　is　carried　out　by　a　second　order　explicit　Runge-Kutta　method.　An　optimal　error　estimate　O(h(2))　in　L-2-norm　for　continuous　linear　finite　elements　is　obtained　under　the　CFL　condition　Delta　t　＜=　Ch(4/3),　Where　h　and　Delta　t　axe　the　spatial　meshsize　and　the　time　step,　respectively,　and　the　positive　constant　C　is　independent　of　h　and　Delta　t.