  We study a new deformed Hermitian Yang-Mills flow on a compact K\"ahler
manifold. We first show the existence of the longtime solution of the flow. We
then show that under the Collins-Jacob-Yau's condition on the subsolution, the
longtime solution converges to the solution of the deformed Hermitian
Yang-Mills equation, which was solved by Collins-Jacob-Yau [5] by the
continuity method. Moreover, as an application of the flow, we show that on a
compact K\"ahler surface, if there exists a semi-subsolution of the deformed
Hermitian Yang-Mills equation, then the flow converges smoothly to a singular
solution to the deformed Hermitian Yang-Mills equation away from a finite
number of curves of negative self-intersection. Such a solution can be viewed
as a boundary point of the moduli space of the deformed Hermitian Yang-Mills
solutions for a given K\"ahler metric.
