  In this paper, we introduce a flow over the projective bundle $p:P(E^*)\to
M$, which is a natural generalization of both Hermitian-Yang-Mills flow and
K\"ahler-Ricci flow. We prove that the semipositivity of curvature of the
hyperplane line bundle $\mathcal{O}_{P(E^*)}(1)$ is preserved along this flow
under the null eigenvector assumption. As applications, we prove that the
semipositivity is preserved along the this flow if the base manifold $M$ is a
curve, which implies that the Griffiths semipositivity is preserved along the
Hermitian-Yang-Mills flow over a curve. And we also reprove that the
nonnegativity of holomorphic bisectional curvature is preserved under
K\"ahler-Ricci flow.
