High-efficiency acceleration of charged particle beams at high gradients of energy gain per unit length is necessary to achieve an affordable and compact high-energy collider. The plasma wakefield accelerator is one concept being developed for this purpose. In plasma wakefield acceleration, a charge-density wake with high accelerating fields is driven by the passage of an ultra-relativistic bunch of charged particles (the drive bunch) through a plasma. If a second bunch of relativistic electrons (the trailing bunch) with sufficient charge follows in the wake of the drive bunch at an appropriate distance, it can be efficiently accelerated to high energy. Previous experiments using just a single 42-gigaelectronvolt drive bunch have accelerated electrons with a continuous energy spectrum and a maximum energy of up to 85 gigaelectronvolts from the tail of the same bunch in less than a metre of plasma. However, the total charge of these accelerated electrons was insufficient to extract a substantial amount of energy from the wake. Here we report high-efficiency acceleration of a discrete trailing bunch of electrons that contains sufficient charge to extract a substantial amount of energy from the high-gradient, nonlinear plasma wakefield accelerator. Specifically, we show the acceleration of about 74 picocoulombs of charge contained in the core of the trailing bunch in an accelerating gradient of about 4.4 gigavolts per metre. These core particles gain about 1.6 gigaelectronvolts of energy per particle, with a final energy spread as low as 0.7 per cent (2.0 per cent on average), and an energy-transfer efficiency from the wake to the bunch that can exceed 30 per cent (17.7 per cent on average). This acceleration of a distinct bunch of electrons containing a substantial charge and having a small energy spread with both a high accelerating gradient and a high energy-transfer efficiency represents a milestone in the development of plasma wakefield acceleration into a compact and affordable accelerator technology.