As a new computing paradigm, processing in memory (PIM) allows the parallel computation in both processors and memories, which drastically reduce the movements between computation units and storage units. Therefore, PIM can be considered as an efficient technology to somewhat address the shortcomings of the von neumann architecture. Compared with traditional random access memories, racetrack memory has many merits including high density, non-volatility, and low static power. Therefore, it can be used for efficient PIM computing. To address the shortages of domain-wall based PIM, this paper proposes a novel PIM framework based on the Skyrmion material. In this framework, we use Skyrmion-based racetrack memories to construct storage units, and use Skyrmion-based logic gates to compose both adders and multipliers for the computation units. Since our framework does not need CMOS (complementary metal oxide semiconductor) circuits to assist the underlying computation unit construction, the design complexity is significantly reduced. Meanwhile, based on our proposed optimization methods for read and write operations at the circuit layer and address mapping mode of the memory at the system level, the performance of our framework is drastically improved. Experimental results show that compared with domain-wall based PIM framework, our approach can achieve 48.1% time improvement and 42.9% energy savings on average.