  The inclination distribution of circumbinary planets (CBPs) is an important
scientific issue. It is of great significance in estimating the occurrence rate
of CBPs and studying their formation and evolution. Although the CBPs currently
discovered by the transit method are nearly coplanar, the true inclination
distribution of CBPs is still unknown. Previous researches on CBPs mostly
regarded them as an isolated binary-planet system, without considering the
birth environment of their host binaries. It is generally believed that almost
all stars are born in clusters. Therefore, it is necessary to consider the
impact of the close encounters of stars on the CBP systems. This article
discusses how the close encounters of fly-by stars affect the inclination of
CBP. Based on extensive numerical simulations, we found that CBPs in close
binary with a spacing of about 0.2 au are almost unaffected by star fly-bys.
Their orbits remain coplanar. However, when the spacing of the binary stars is
greater than 1 au, the 2-3 fly-bys of the intruding star can excite a
considerable inclination even for the CBP near the unstable boundary of the
binary. For the planets in the outer region, a single star fly-by can excite an
inclination to more than 5 degrees. Especially, CBPs in near polar or
retrograde orbits can naturally form through bianry-star encounters. If close
binaries are born in open clusters, our simulations suggest that there may be
high-inclination CBPs in binaries with spacing > 1 au.
