Certain n-qubit quantum systems can be faithfully simulated by quantum circuits with only O(log(n)) qubits [B. Kraus, Phys. Rev. Lett. 107, 250503 (2011)]. Here we report an experimental realization of this compressed quantum simulation on a one-dimensional Ising chain. By utilizing an nuclear magnetic resonance quantum simulator with only five qubits, the property of ground-state magnetization of an open-boundary 32-spin Ising model is experimentally simulated, prefacing the expected quantum phase transition in the thermodynamic limit. This experimental protocol can be straightforwardly extended to systems with hundreds of spins by compressing them into up to merely 10-qubit systems. Our experiment paves the way for exploring physical phenomena in large-scale quantum systems with quantum simulators under current technology.