In this paper we investigate two-dimensional ( 2D ) Rayleigh-Bénard convection using direct numerical simulation in Boussinesq fluids of Prandtl number P = 6.8 confined between thermally conducting plates . We show through the simulation that in a small range of reduced Rayleigh number r ( 770 < r < 890 ) the 2D rolls move chaotically in a direction normal to the roll axis . The lateral shift of the rolls may lead to global flow reversal of the convective motion . The chaotic traveling rolls are observed in simulation with free-slip as well as no-slip boundary conditions on the velocity field . We show that the traveling rolls and the flow reversal are due to an interplay between the real and imaginary parts of the critical modes .