  In this paper, we provide a recipe for computing Euler number of Grassmann
manifold G(k,N) by using Mathai-Quillen formalism (MQ formalism) and
Atiyah-Jeffrey construction. Especially, we construct path-integral
representation of Euler number of G(k,N). Our model corresponds to a finite
dimensional toy-model of topological Yang-Mills theory which motivated
Atiyah-Jeffrey construction. As a by-product, we construct free fermion
realization of cohomology ring of G(k,N).
