A major milestone for the LHC Accelerator Research Program (LARP) is the test, by the end of 2009, of two 4 m-long quadrupole magnets (LQ) wound with Nb3Sn conductor. The goal of these magnets is to be a proof of principle that Nb3Sn is a viable technology for a possible LHC luminosity upgrade. The design of the LQ is based on the design of the LARP Technological Quadrupoles, presently under development at FNAL and LBNL, with 90-mm aperture and gradient higher than 200 T/m. The design of the first LQ model will be completed by the end of 2007 with the selection of a mechanical design. In this paper we present the coil design addressing some fabrication technology issues, the quench protection study, and three designs of the support structure.