Mg11B2 has a great application prospect in the superconducting coils for fusion reactor as the "low activation superconductors". The un-doped Mg11B2 and Cu-doped Mg11B2 bulks using 11B as a boron precursor were fabricated by low-temperature sintering in present work. It was found that the prepared Mg11B2 low activation superconductors exhibit better Jc performance than all of other Mg11B2 samples reported in previous studies. As for Cu doped Mg11B2, minor Cu addition can obviously improve the Mg11B2 grain crystallization and reduce the amount of MgO impurity. Hence, improved grain connectivity and higher Jc at low fields is obtained in Cu doped Mg11B2 samples. For un-doped samples, refined grains and more MgO impurity with proper size brought about more flux pinning centers, resulting in better Jc performance at high fields.