The robustness of urban bus-transport networks has important influence on the network performance. This paper proposes the model of layered public bus-transport network which is composed of the logical layer and the physical layer and expounds the relationship between these two layers. We map the bus-transport network into two spaces: space P and space L and take space P as logical layer while space L as physical layer. We define the load of edges in the physical layer according to the traffic flow in the logical layer and assume that a removed edge only leads to a redistribution of the load through it to its neighboring edges. We analysis the robustness of layered public bus-transport networks in the face of cascading failure under the case of removing the edge with the highest load and redistributing of the load. Through the simulation of the public bus-transport networks of three major cities in China, we find that in the layered public bus-transport network the traffic flow in the logical layer affects the distribution of load of edges in the physical layer. The removal of the edge with the highest load may lead to the cascading failures of the physical layer, and the avalanche size decreases with the increase of the tolerance parameter.