  Baryon acoustic oscillation (BAO) is one of the important standard ruler in
cosmology. The results of the latest BAO measurements by Dark Energy
Spectroscopic Instrument (DESI) survey has been reported. Cosmology with the
varying electron mass model and the early dark energy (EDE) models are regraded
as interesting models to resolve the Hubble tension. We present constraints on
the varying electron mass model and EDE models by including new DESI data as
well as cosmic microwave background by Planck and the conventional BAO data
from 6dF, MGS, and DR12 and supernovae light curve data into analysis. Since
new DESI BAO data indicates slightly longer sound horizon $r_dh$ than the other
BAO observations, for the varying electron mass model, the larger $H_0
=69.44\pm 0.84 $ km$/$s$/$Mpc is indicated.
