  Interstellar dust extinction law is essential for interpreting observations.
In this work, we investigate the ultraviolet (UV)--mid-infrared (IR) extinction
law of the Taurus molecular cloud and its possible variations. We select
504,988 dwarf stars (4200 K < Teff < 8000 K) and 4,757 giant stars (4200 K <
Teff < 5200 K) based on the stellar parameters of Gaia DR3 as tracers. We
establish the Teff--intrinsic color relations and determine the intrinsic color
indices and color excesses for different types of stars. In the determination
of color excess ratios (CERs), we analyze and correct the curvature of CERs and
derive the UV--mid-IR CERs of 16 bands. We consider different effective
wavelengths for different types of stars when converting CERs to relative
extinction, and obtain the extinction law with a better wavelength resolution.
In addition, we analyze the possible regional variation of extinction law and
derive the average extinction law of Rv=3.13+-0.32 for the Taurus molecular
cloud. Only 0.9% of subregions have deviations >3sigma, indicating limited
regional variation in the extinction law. We also discuss the effect of Gaia
Teff overestimation on the determination of the Taurus extinction law and find
that the effect is negligible.
