La0.5Ca0.5MnO3 (LCMO) polycrystalline sample was synthesized by the solid-state reaction method. The result of X-ray diffraction shows that the LCMO is single phase. We have studied the magnetic response of charge-ordered (CO) state in the LCMO manganite. The magnetic hysteresis loop at 100 K displays an interesting butterfly-type structure, which indicates the existence of CO anti-ferromagnetic (AFM) structure in LCMO. The temperature-dependent magnetization measurements show a paramagnetic (PM) to ferromagnetic (FM) transition at Curie temperature (TC ≈ 130 K) and a FM to AFM transition at Neel temperature (TN ≈ 50 K), measured under different fields of 100, 500 and 5000 Oe. Moreover, there is an interesting intercross in zero-field cooling (ZFC) and filed-cooling (FC) measurements, i.e., an intercross of the ZFC/FC curves in the CO LCMO manganite. These present magnetism measurements are discussed and possible explanations are provided by the existence of CO AFM state.