  The Hubble constant, $H_0$, which is a crucial parameter in astrophysics and
cosmology, is under significant tension. We explore an independent technique to
measure $H_0$ based on the time-delay cosmography with strong gravitational
lensing of a supernova lensed by a galaxy cluster, focusing on SN Refsdal in
MACS J1149.5+2223, the first gravitationally lensed supernova with resolved
multiple images. We carefully examine the dependence of constraints on the
Hubble constant on the choice of lens mass models, employing 23 lens mass
models with different assumptions on dark matter halos and external
perturbations. Remarkably, we observe that the dependence on the choice of lens
mass models is not significantly large, suggesting the robustness of the
constraint on the Hubble constant from SN Refsdal. We combine measurements for
the 23 lens mass models to obtain $H_0=70.0^{+4.7}_{-4.9}km/s/Mpc$ assuming
equal weighting. We find that best-fitting Hubble constant values correlate
with radial density profiles of the lensing cluster, implying a room for
improving the constraint on the Hubble constant with future observations of
more multiple images. We also find a clear correlation between best-fitting
Hubble constant values and magnification factors of supernova multiple images.
This correlation highlights the importance of gravitationally lensed Type Ia
supernovae for accurate and robust Hubble constant measurements.
