  In this paper, we firstly construct $\pi$-type Fermions. According to these,
we define $\pi$-type Boson-Fermion correspondence which is a generalization of
the classical Boson-Fermion correspondence. We can obtain $\pi$-type symmetric
functions $S_\lambda^\pi$ from the $\pi$-type Boson-Fermion correspondence,
analogously to the way we get the Schur functions $S_\lambda$ from the
classical Boson-Fermion correspondence (which is the same thing as the
Jacobi-Trudi formula). Then as a generalization of KP hierarchy, we construct
the $\pi$-type KP hierarchy and obtain its tau functions.
