  Fault-tolerant implementation of quantum gates is one of preconditions for
realizing quantum computation. The platform of Rydberg atoms is one of the most
promising candidates for achieving quantum computation. We propose to implement
a controlled-$Z$ gate on Rydberg atoms where an amplitude-modulated field is
employed to induce Rydberg antiblockade. Gate robustness against the
fluctuations in the Rydberg-Rydberg interaction can be largely enhanced by
adjusting amplitude-modulated field. Furthermore, we introduce a
Landau-Zener-St\"{u}ckelberg transition on the target atom so as to improve the
gate resilience to the deviation in the gate time and the drift in the pulse
amplitude. With feasible experimental parameters, one can achieve the gate with
low fidelity errors caused by atomic decay, interatomic dipole-dipole force,
and Doppler effects. Finally, we generalize the gate scheme into multiqubit
cases, where resilient multiqubit phase gates can be obtained in one step with
an unchanged gate time as the number of qubits increases.
