Quantum computers can efficiently solve classically intractable problems, such as the factorization of a large number1 and the simulation of quantum many-body systems2,3. Universal quantum computation can be simplified by decomposing circuits into single- and two-qubit entangling gates4, but such decomposition is not necessarily efficient. It has been suggested that polynomial or exponential speedups can be obtained with global N-qubit (N greater than two) entangling gates5-9. Such global gates involve all-to-all connectivity, which emerges among trapped-ion qubits when using laser-driven collective motional modes10-14, and have been implemented for a single motional mode15,16. However, the single-mode approach is difficult to scale up because isolating single modes becomes challenging as the number of ions increases in a single crystal, and multi-mode schemes are scalable17,18 but limited to pairwise gates19-23. Here we propose and implement a scalable scheme for realizing global entangling gates on multiple 171Yb+ ion qubits by coupling to multiple motional modes through modulated laser fields. Because such global gates require decoupling multiple modes and balancing all pairwise coupling strengths during the gate, we develop a system with fully independent control capability on each ion14. To demonstrate the usefulness and flexibility of these global gates, we generate a Greenberger-Horne-Zeilinger state with up to four qubits using a single global operation. Our approach realizes global entangling gates as scalable building blocks for universal quantum computation, motivating future research in scalable global methods for quantum information processing.