The homotopy theoretic method has been applied to the algebraic cycle theory for a long period of time. In particular, it can be applied to compute topological invariants of Chow varieties. In this talk I will discuss this method in calculating the Euler Characteristic of Chow varieties. The calculation in a direct and simple way (this result has been obtained by Blaine Lawson and Stephen Yau in a different way). This technique also can be applied to Chow varieties with certain group actions and other cases. Furthermore, I will also talk about the application of the method on $l$-adic Euler-Poincare Characteristic of Chow varieties over arbitrary algebraic closed field.