This paper develops a convex quadratic programming (QP) formulation for the demand response (DR) optimization of plug-in hybrid electric vehicles (PHEVs) under time-varying electricity price signals. The work is motivated by the need for a computationally-efficient PHEV DR model that accounts for the ohmic energy losses in PHEV batteries, and is scalable to large-scale vehicle-to-grid (V2G) optimization and control applications. We use a previously-developed power-split PHEV model with an optimal power management strategy to compute the average distance-based PHEV energy consumption characteristics. Moreover, we use an equivalent circuit battery model for the PHEV's charge and discharge process. We then derive the PHEV's total fuel and electric energy cost as a quadratic function of battery state-of-charge (SOC), and show that the cost function is convex. Finally, we use a standard QP solver to optimize the PHEV's demand response for a few sample trips obtained from the U.S. National Household Travel Survey (NHTS) dataset. The achieved optimization time for a 24-hour time window with 5 min. resolution is less than 0.1 s (using a single quad-core computer). The method can hence be easily scaled for large-scale smart grid optimization and control studies.