Studies of the Spin-Seebeck effect (SSE) are very important for the developments of fundamental science and novel low-power-consumption technologies. Spin-Seebeck diode (SSD), in which the spin current can be driven by a forward temperature gradient but not by a reverse temperature gradient, is a key unit in spin caloritronic devices. Here, we propose a new design of SSD using two-dimensional (2D) materials such as the silicene and phosphorene nanoribbons as the source and drain. Due to their unique band structures and magnetic states, thermally driven spin-up and spindown currents flow in opposite directions. This mechanism is different from that of the previous one that uses two Permalloy circular disks [Phys. Rev. Lett. 2014, 112, 047203], and the SSD in our design can be easily integrated with gate voltage control. Since the concept of this design is rather general and applicable to many 2D materials, it is promising for the realization and exploitation of SSD in nanodevices. PACS number(s): 73.23.Hk