  For two complex vector bundles admitting a homomorphism between them, a
Poincar\'e-Hopf formula for the difference of the Chern character numbers of
these two vector bundles with isolated singularities is established by Huitao
Feng, Weiping Li and Weiping Zhang. This article extend their reslut about
Poincar\'e-Hopf type formula for the difference of the Chern character numbers
to the non-isolated singularities. A special connection
$\widetilde{\nabla}_{1}^{E}$ be constructed, the Chern character ${\rm
ch}(E,\widetilde{\nabla}_{1}^{E})$ is the key role for the non-isolated
singularities. As a consequence, a Poincar\'e-Hopf type formula for a pair of
vector field with the function $h^{T_{\mathbb{C}}M}(\cdot,\cdot)$ has
non-isolated zero points over a closed, oriented smooth manifold of dimension
$2n$ is established.
