This study introduces a high-precision geometric positioning method for high-resolution optical satellite imagery that does not rely on ground control points (GCPs), utilizing preconditioned conjugate gradient (PCG) and graphics processing unit (GPU) acceleration. The core technologies used in this method include an adjustment model that is constructed based on virtual control points (VCPs), a sparse matrix storage format, and parallel block adjustment accelerated by PCG-GPU. By employing a sparse matrix storage format to reduce computer memory requirements, PCG-GPU parallel acceleration technology enhances the efficiency of block adjustment parameter processing. Experimental verification is performed using 829 Ziyuan-3 (ZY-3) satellite images from Jiangxi area. The results show that the proposed PCG-GPU accelerated parallel block adjustment method is approximately 9.5 times more efficient than traditional serial computing methods. In addition, following block adjustment, the root mean square error (RMSE) is 0.461 pixel and 0.652 pixel in the x and y directions, respectively, which meets the stringent accuracy requirements for high-precision satellite image mapping.