Abstract: The regularity for the 2D incompressible MHD equations with partial dissipation and magnetic diffusion was studied.A regularity criteria was given for the 2D incompressible MHD equations with partial dissipation and magnetic diffusion(The velocity field and the magnetic field had the partial derivative of two-order type only in the same one direction).It is proved that the uniqueness local classical solution of the 2D incompressible MHD equations with partial dissipation and magnetic diffusion will be global if the partial derivative of magnetic in one direction satisfies one regularity criteria.