Abstract: A new adaptive grid technique is proposed, which can redistribute grid points according to the equivalence of area under the curve of the weight function. So the iteration in the traditional technique through a variational approach is unnecessary here, and the efficiency is improved greatly. The new technique is applied to Burgers equation with analytic solutions. The results show that different weight functions have different distribution of grid points, and variational weight functions with time have variational distribution of grid points. Because the new technique can redistribute more grid points in the high gradient solution regions in response to the numerical solution, it can capture the shock efficiently.