Abstract: The application of spatial data is becoming increasingly large. Interpolation can effectively reconstruct the unknown data in space, which is actually a process of data reproduction, and also a process of reproducing data with higher resolution from original data. Interpolation methods are divided into two branches: definite interpolation and indefinite interpolation. On one hand, the uncertainty of indefinite interpolation shows in selecting certain stochastic interpolation ways; on the other hand, the uncertainty is reflected by selecting the interpolation parameters using probability principles. Multiple-point simulation(MPS) is an important indefinite interpolation method in reconstructing spatial data, and single normal equation simulation(SNESIM), as a frequently used MPS method, has been used in three-dimensional reconstruction of categorical spatial data in many fields currently. However, due to the large burdens on CPU and memory brought in by SNESIM, its practical application has been limited greatly. To overcome this limitation, SNESIM is parallelized using compute unified device architecture(CUDA). A proper size of data template is chosen using the entropy theory of training image (TI) and the reconstruction quality is improved by the integration of soft data and hard data. Compared with the CPU-based SNESIM method, the CUDA-based one shows the better reconstruction efficiency of spatial data.