In order to solve the dynamic and heterogeneous storage of distributed storage systems, this paper proposes a construction algorithm of heterogeneous fractional repetition codes based on node common edge (HFRC-NCE) is proposed in this paper. In particular, the data blocks encoded by MDS code are divided into cold and hot data blocks, which are copied and stored with different multiples in storage nodes. Moreover, combined with the characteristic of node common edge, the structure of the heterogeneous fractional repetition codes is more simple and intuitive, which can realize the precise non-coding repair of fault nodes. Compared with the fractional repetition codes constructed by complete graph and partial regular graph, theoretical analyses show that, although the storage overhead and bandwidth overhead of HFRC-NCE are a litter larger, its node repair options are larger and the node storage capacities are more diverse. Meanwhile, The reconstruction degree of HFRC-NCE is much smaller.