A data processing system and method for accessing a heterogeneous memory system including a processing unit are provided. The heterogeneous memory system includes a memory module and high bandwidth memory (HBM) including a processing-in-memory (PIM) circuit combined with a memory controller. The memory controller is configured to detect a data array required for an arithmetic operation from a memory module or the HBM by using a border index value when the arithmetic operation is performed by the PIM circuit of the HBM and generate a memory module command set and an HBM command set using physical address spaces respectively designated in the memory module and the HBM.