Plasma-based accelerators driven by either intense lasers1 or charged particle beams2 can accelerate electrons or positrons with extremely high gradients compared with conventional radio-frequency accelerators. For their use as next-generation light sources and in energy frontier colliders3, beams with good stability, high quality, controllable polarization and excellent reproducibility4,5 are required. The accelerated electrons can be either internally injected directly from the background plasma or externally injected from conventional accelerators. Despite significant progress6–14, the beam properties obtained with the internal injection scheme fall short of simultaneously reaching these requirements. In contrast, such high-property beams are routinely generated from conventional accelerators. Therefore, it is important to demonstrate the injection from a conventional accelerator into a plasma-based machine followed by further acceleration of the beam. Here we report the demonstration of external injection from a conventional linear accelerator into a laser wakefield accelerator and subsequent acceleration without any significant loss of charge, which is achieved by properly shaping and matching the beam into the plasma structure. The experimental results, combined with three-dimensional particle-in-cell simulations, indicate that this is possible with modest degradation in the beam quality. This work is an important step towards realizing a high-throughput, multistage, high-energy, hybrid conventional-plasma-based accelerator.