High-precision integer multiplication is crucial in privacy-preserving computational techniques but poses acceleration challenges on GPUs due to its complexity and the diverse bit lengths in cryptosystems. This paper introduces \GIM, an efficient high-precision integer multiplication algorithm accelerated with GPUs. It employs a novel segmented integer multiplication algorithm that separates implementation details from bit length, facilitating code optimizations. We also present a computation diagram to analyze parallelization strategies, leading to a series of enhancements. Experiments demonstrate that this approach achieves a 4.47x speedup over the commonly used baseline.