Semiconductor laser (SL) with optical feedback presents rich nonlinear dynamics, e.g., period-one oscillation (POO), quasi-periodic oscillation, and chaotic states. It is of significance to study the state boundary between different dynamic states for an SL with optical feedback from the perspective of both suppressing and using these dynamics, especially the boundary of POO state. This paper reveals the POO boundary of an SL with dual optical feedback (DOF). The modified Lang-Kobayashi equations were first numerically solved to develop a bifurcation diagram to determine the boundary between POO and other states. Then the POO-DOF boundary was compared with that of an SL with single optical feedback. Moreover, the effect of system parameters on the POO-DOF boundaries is researched. The results obtained are helpful to promote the development of the applications of POO dynamics.