In this talk, we are concerned with variational inequalities for p-Laplacian type parabolic equations with irregular double obstacles. The values of solutions under consideration are required to have two-sided constraints. We discuss parabolic double obstacle problems to establish the global Calderon-Zygmund type estimates for such solutions. In particular, the existence of such a solution shall be dealt with carefully as this solution is prescribed to satisfy the associated parabolic variational inequality instead of the parabolic equation.