Recent developments of hybrid vehicle technology have promoted another wave of vehicle electrification and introduction of pure electric vehicles (PEVs), such as Nissan Leaf and Ford Transit Connect Electric. The energy efficiency of these PEVs with an electric drive can be potentially further improved by introducing a two-speed or multi-speed gearbox to ensure the electric machine to operate at peak performance. In this work, a powertrain model of the Transit Connect Electric is built to examine the powertrain efficiency improvement potentials using a two-speed gearbox. The HEV and EV powertrain modeling tool, AUTONOMIE from US Argonne National Lab, is used for the powertrain modeling, and partially verified using vehicle testing data from US Environment Protection Agency (EPA). An optimization method, whose kernel is Dynamic Programming (DP), is combined with the model to find the possible minimum energy consumption and corresponding gear ratios. The electric drive designs: a) with or without a two-speed gearbox; and b) using original rule-based gearshift controller or using DP-improved gearbox controller, are compared and analyzed. This study can facilitate a better understanding on the PEVs' powertrain efficiency and provide guidelines to cost-effective PEV electric drive design for given driving cycles using an appropriate electric machine. The need and benefit of two-speed gearbox for mixed city and highway driving are explored. The study forms a foundation for further research in this area.