The Iterative Closest Point (ICP) algorithm suffers from sensitivity to outliers and tendency to local optima in point cloud fine registration. In this paper, we introduce a global and robust ICP framework called Granular-Ball Iterative Closest Point with MultiKernel Correntropy (GRICP). This approach transforms the point cloud into a granular ball cloud and employs MultiKernel Correntropy (MKC) as the loss function, which is designed to smooth out the effects of noise points and provide global information for registration. Specifically, we propose a coarse-grained representation of the point cloud using the granular ball model, which adaptively captures the coarse-grained features of the data and converts the point cloud into a multi-granularity ball cloud. The normal points within each granular ball help mitigate the influence of noise points. To ensure that ICP finds the globally optimal transformation, MKC is introduced to measure the distribution of registration errors, thereby offering global insights for ICP to achieve the optimal solution. The transformations based on MKC and the granular ball cloud are then derived. Extensive experiments on both simulated and real-world datasets demonstrate that GRICP delivers superior registration performance, particularly in scenarios involving large rotation offsets, partial overlaps, and Gaussian noise.