This letter reports the first experimental demonstration of the quantum Mpemba effect (QMPE) in a trapped-ion quantum simulator. The QMPE is a phenomenon where a system with a greater degree of symmetry breaking restores its symmetry more rapidly compared to a system with less symmetry breaking. The study uses a $N=12$ qubit trapped-ion quantum simulator to investigate the QMPE in a chain of spins coupled via power-law decaying interactions. The symmetry breaking and restoration are monitored through entanglement asymmetry (EA), which is probed via randomized measurements and post-processed using the classical shadows technique. The findings are further supported by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, providing direct evidence of subsystem thermalization. The experiment shows that the QMPE occurs in a non-integrable system and is robust against decoherence and disorder, marking a significant advancement in understanding the dynamics of many-body quantum systems.This letter reports the first experimental demonstration of the quantum Mpemba effect (QMPE) in a trapped-ion quantum simulator. The QMPE is a phenomenon where a system with a greater degree of symmetry breaking restores its symmetry more rapidly compared to a system with less symmetry breaking. The study uses a $N=12$ qubit trapped-ion quantum simulator to investigate the QMPE in a chain of spins coupled via power-law decaying interactions. The symmetry breaking and restoration are monitored through entanglement asymmetry (EA), which is probed via randomized measurements and post-processed using the classical shadows technique. The findings are further supported by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, providing direct evidence of subsystem thermalization. The experiment shows that the QMPE occurs in a non-integrable system and is robust against decoherence and disorder, marking a significant advancement in understanding the dynamics of many-body quantum systems.