  Single Degenerate model is the most widely accepted progenitor model of type
Ia supernovae (SNe Ia), in which a carbon-oxygen white dwarf (CO WD) accretes
hydrogen-rich material from a main sequence or a slightly evolved star (WD +MS)
to increase its mass, and explodes when its mass approaches the Chandrasekhar
mass limit. During the mass transfer phase between the two components, an
optically thick wind may occur and the material lost as the wind may exist as
circumstellar material (CSM). Searching the CSM around progenitor star is
helpful to discriminate different progenitor models of SNe Ia. Meanwhile, the
CSM is a source of color excess.The purpose of this paper is to study the color
excess produced from the single-degenerate progenitor model with optically
thick wind, and reproduce the distribution of color excesses of SNe Ia. Meng et
al. (2009) systemically carried out binary evolution calculation of the WD +MS
systems for various metallicities and showed the parameters of the systems
before Roche lobe overflow and at the moment of supernova explosion in Meng &
Yang (2009). With the results of Meng et al. (2009), we calculate the color
excesses of SNe Ia at maximum light via a simple analytic method.We reproduces
the distribution of color excesses of SNe Ia by our binary population synthesis
approach if the velocity of the optically thick wind is taken to be of order of
magnitude of 10 km s$^{\rm -1}$. However, if the wind velocity is larger than
100 km s$^{\rm -1}$, the reproduction is bad.
