© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This paper proposes a novel parcel delivery system which consists of a drone and public transportation vehicles such as trains, trams, etc. This system involves two delivery schemes: drone-direct scheme referring to delivering to a customer by a drone directly and drone–vehicle collaborating scheme referring to delivering a customer based on the collaboration of a drone and public transportation vehicles. The fundamental characteristics including the delivery time, energy consumption and battery recharging are modelled, based on which a time-dependent scheduling problem for a single drone is formulated. It is shown to be NP-complete and a dynamic programming-based exact algorithm is presented. Since its computational complexity is exponential with respect to the number of customers, a sub-optimal algorithm is further developed. This algorithm accounts the time for delivery and recharging, and it first schedules the customer which leads to the earliest return. Its computational complexity is also discussed. Moreover, extensive computer simulations are conducted to demonstrate the scheduling performance of the proposed algorithms and the impacts of several key system parameters are investigated.