The network load is increasing due to the spread of content distribution services. Caching is known as a technique to reduce a peak network load by prefetching popular contents into memories of users. Coded caching is a new caching approach based on a carefully designed content placement in order to create coded multicasting opportunities. Recent works have discussed single-layer caching systems, but many networks consist of multiple layers of cache. In this paper, we discuss a coded caching problem for a hierarchical network that has a different number of layers of cache. The network has users who connect to an origin server via a mirror server and users who directly connect to the origin server. We provide lower bounds of the rates for this problem setting based on the cut-set bound. In addition, we propose three basic coded caching schemes and characterize these schemes. Also, we propose a new coded caching scheme by combining two basic schemes and provide achievable rates of the combination coded caching scheme. Finally, we show that the proposed combination scheme demonstrates a good performance by a numerical result.