The New Horizons mission is progressing toward its planned launch in January 2006. Current plans call for the New Horizons spacecraft to be launched by a newly developed evolved expendable launch vehicle (EELV) Atlas V 551 with the STAR 48B kick stage in January/February 2006. After flying for more than 32 AU and traveling through the inner and outer solar system, the spacecraft is expected to arrive at Pluto as early as July 2015 for the first scientific reconnaissance investigations of the last planet that has not yet been visited by a spacecraft. This paper describes the baseline mission design, which includes the baseline launch scenario that maximizes the launch probability with an extensive launch period of 35 days, the interplanetary trajectory design that allows the spacecraft to fly fast to Pluto by taking advantage of the gravity assist from Jupiter, the trajectory design of the close encounter with Pluto and its moon Charon, and the mission plan for the extended mission beyond Pluto to fly by a Kuiper belt object. Note: New Horizons is NASA's planned mission to Pluto and has not been approved for launch. All representations in this paper are contingent on a decision by NASA to go forward with the preparation for and launch of the mission.