In general-purpose particle detectors, the particle-flow algorithm may be used to reconstruct a comprehensive particle-level view of the event by combining information from the calorimeters and the trackers, significantly improving the detector resolution for jets and the missing transverse momentum. In view of the planned high-luminosity upgrade of the CERN Large Hadron Collider (LHC), it is necessary to revisit existing reconstruction algorithms and ensure that both the physics and computational performance are sufficient in an environment with many simultaneous proton-proton interactions (pileup). Machine learning may offer a prospect for computationally efficient event reconstruction that is well-suited to heterogeneous computing platforms, while significantly improving the reconstruction quality over rule-based algorithms for granular detectors. We introduce MLPF, a novel, end-to-end trainable, machine-learned particle-flow algorithm based on parallelizable, computationally efficient, and scalable graph neural networks optimized using a multi-task objective on simulated events. We report the physics and computational performance of the MLPF algorithm on a Monte Carlo dataset of top quark-antiquark pairs produced in proton-proton collisions in conditions similar to those expected for the high-luminosity LHC. The MLPF algorithm improves the physics response with respect to a rule-based benchmark algorithm and demonstrates computationally scalable particle-flow reconstruction in a high-pileup environment.