We demonstrate the efficient internal shock dissipation through the multiple interactions between magnetized relativistic jets with weakly magnetized winds by our implemented spherically symmetrical one-dimensional special relativistic magneto-hydrodynamic simulation. We estimated an energy dissipation efficiency through multiple interactions with alternately injected magnetized jets and weakly magnetized winds. Our numerical results show the magnetic energy of the jet is converted into the kinetic energy of the shocked external medium by the magnetic pressure, then dissipated into the internal energy by the shock waves. Multiple magnetic energy conversion processes can produce kinetically dominated relativistic outflows with almost 10¥% average dissipation efficiency. Such outflows are relevant for observed non-thermal emissions in blazars or gamma-ray bursts.