We will discuss the topological properties of the independence complex of Kneser graphs, Ind(KG$(n,k))$, with $n\ge 3$ and $k\ge 1$. By identifying one kind of maximal simplices through projective planes, we obtain homology generators for the $6$-dimensional homology of the complex Ind(KG$(3,k))$. Using cross-polytopal generators, we provide lower bounds for the rank of $p$-dimensional homology of the complex Ind(KG$(n,k))$ where $p=1/2\cdot (\genfrac{}{}{0ex}{}{2n+k}{2n})$.