A compact 400-MHz half-wave spoke resonator (HWSR) superconducting crab cavity is being developed for the LHC upgrade. The cavity shape and the LOM/HOM couplers for such a design have been optimized to meet the space and beam dynamics requirements, and satisfactory RF parameters have been obtained. As it is known that multipacting is an issue of concern in a superconducting cavity which may limit the achievable gradient. Thus it is important in the cavity RF design to eliminate the potential MP conditions to save time and cost of cavity development. In this paper, we present the multipacting analysis for the HWSR crab cavity using the Track3P code developed at SLAC, and to discuss means to mitigate potential multipacting barriers. Show Partial Abstract