  A cosmological model with a time-varying mass of electrons seems a promising
solution for the so-called Hubble tension. We examine the big bang
nucleosynthesis (BBN) constraints on the time-varying electron mass model,
because a larger electron mass gives rise to the smaller neutron decay rate
which could affect the light element abundance. Additionally, different
inferred cosmological parameters, primarily baryon asymmetry, to keep the
cosmic background power spectrum unchanged could affect the abundance of light
element. We find that the predicted helium fraction becomes larger and the
deuterium abundance becomes smaller as the electron mass at the BBN time
becomes larger. Thus, we conclude that an acceptable electron mass at the BBN
time would be only approximately 1% greater than the current electron mass.
