In this article, we study the implications of the coupling between Axion-Like-Particles (ALPs) and Leptons to cosmology, in particular, the Big Bang Nucleosynthesis (BBN). We show that the BBN, through the constraint on the effective number of relativistic neutrino species, provides the most stringent bound on the ALP-electron interaction strength for the mass of axion between 20 keV and 1 MeV. For other values of the mass, the BBN bound complements the stellar-evolution and laboratory bounds.