  Inevitable interactions with the reservoir largely degrade the performance of
non-local gates, which hinders practical quantum computation from coming into
existence. Here we experimentally demonstrate a 99.920(7)\%-fidelity
controlled-NOT gate by suppressing the complicated noise in a solid-state spin
system at room temperature. We found that the fidelity limited at 99\% in
previous works results from only considering static noise, and thus, in this
work, time-dependent noise and quantum noise are also included. All noises are
dynamically corrected by an exquisitely designed shaped pulse, giving the
resulting error below $10^{-4}$. The residual gate error is mainly originated
from the longitudinal relaxation and the waveform distortion that can both be
further reduced technically. Our noise-resistant method is universal, and will
benefit other solid-state spin systems.
