There is a growing interest for the search of new light gauge bosons. The small mass of a new boson can turn various kinds of low-energy experiments to a new discovery machine, depending on their couplings to the Standard Model particles. It is important to understand the properties of each type of gauge boson and their current constraints for a given mass. While the dark photon (which couples to the electric charges) and the U(1)(B-L) gauge boson have been well studied in an extensive mass range, the U(1)(L) gauge boson has not been fully investigated yet. We consider the gauge boson of the U(1)(L) in a wide mass range m(Z') approximate to 0-10(12) eV and investigate the constraints on its coupling from various experiments, discussing the similarities and differences from the dark photon and the U(1)(B-L) gauge boson.