The best-performing brain-machine interfaces (BMIs) to date decode movement intention from intracortically recorded spikes, but these signals may be lost over time. A way to increase the useful lifespan of BMIs is to make more comprehensive use of available neural signals. Recent studies have demonstrated that the local field potential (LFP), a potentially more robust signal, can also be used to control a BMI. However, LFP-driven performance has fallen short of the best spikes-driven performance. Here we report a biomimetic BMI driven by low-frequency LFP that enabled a rhesus monkey to acquire and hold randomly placed targets with 99% success rate. Although LFP-driven performance was still worse than when decoding spikes, to the best of our knowledge this represents the highest-performing LFP-based BMI. We also demonstrate a new hybrid BMI that decodes cursor velocity using both spikes and LFP. This hybrid decoder improved performance over spikes-only decoding. Our results suggest that LFP can complement spikes when spikes are available or provide an alternative control signal if spikes are absent.