The Collaborative International Dictionary of English v.0.48:

Grasping \Grasp"ing\, a.
   1. Seizing; embracing; catching.
      [1913 Webster]

   2. Avaricious; greedy of gain; covetous; close; miserly; as,
      he is a grasping man. -- Grasp"ing*ly, adv. --
      Grasp"ing*ness, n.
      [1913 Webster]