  A quantum algorithm can be decomposed into a sequence consisting of single
qubit and 2-qubit entangling gates. To optimize the decomposition and achieve
more efficient construction of the quantum circuit, we can replace multiple
2-qubit gates with a single global entangling gate. Here, we propose and
implement a scalable scheme to realize the global entangling gates on multiple
$\yb$ ion qubits by coupling to multiple motional modes through external
fields. Such global gates require simultaneously decoupling of multiple
motional modes and balancing of the coupling strengths for all the qubit-pairs
at the gate time. To satisfy the complicated requirements, we develop a
trapped-ion system with fully-independent control capability on each ion, and
experimentally realize the global entangling gates. As examples, we utilize
them to prepare the Greenberger-Horne-Zeilinger (GHZ) states in a single
entangling operation, and successfully show the genuine multi-partite
entanglements up to four qubits with the state fidelities over $93.4\%$.
