  One scheme is presented to construct the robust multi-qubit arbitrary-phase
controlled-phase gate (CPG) with one control and multiple target qubits in
Rydberg atoms using the Lewis-Riesenfeld (LR) invariant method. The scheme is
not limited by adiabatic condition while preserves the robustness against
control parameter variations of adiabatic evolution. Comparing with the
adiabatic case, our scheme does not require very strong Rydberg interaction
strength. Taking the construction of two-qubit $\pi$ CPG as an example, our
scheme is more robust against control parameter variations than non-adiabatic
scheme and faster than adiabatic scheme.
