The invention relates to a robot capable of synchronously climbing stairs. The robot comprises a tray component, a first walking component, a second walking component and a rotation driving device, wherein the tray component comprises a first support member, a second support member and a third support member, of which the mutual distance and height can be adjusted according to stair steps, the first walking component and the second walking component are respectively connected to the lower ends of the first and third support members and are the same in structure, each walking component comprises an axle, a left wheel member and a right wheel member which are located at the two ends of the axle, the two wheel members are symmetric and identical in structure, shape curves of each wheel rim consist of end-to-end-connected Archimedean spirals and arcs, then, the distance from the wheel rims to the axes of the axles is changed along with rotation, and the rotation driving device is mounted at the lower end of the second support member, is in transmission connection with the first walking component and the second walking component respectively and drives the first walking component and the second walking component. The robot can bear a heavy load, keep horizontal, stably and automatically climb the stairs and walk on flat ground.