Based on Maximum Distance Separable (MDS) codes, piggybacking codes can reduce the repair bandwidth overhead of systematic nodes effectively, but there are still problems about larger repair degree, higher repair bandwidth of parity nodes, etc. At the same time, the existing piggybacking codes ignore the differences of hot and cold data in the actual distributed storage systems. For the reason above, a construction of block design-based piggybacking codes is proposed, which can provide more protection for hot data nodes. Specifically, the block design is used to group hot and cold data nodes non-uniformly, in which the hot data symbols are piggybacked into the corresponding parity nodes. Moreover, cold data parity blocks, hot data parity blocks, and slant parity blocks are generated to achieve lower repair bandwidth rate and repair degree rate of nodes. Theoretical analyses and experimental simulations show that, compared with the existing piggybacking codes, the block design-based piggybacking codes reduce the average repair bandwidth rate and average repair degree rate of the failed nodes significantly, and the repair bandwidth overhead of hot data nodes is much lower than cold data nodes.