Receiver arrays with a large number of coil elements are becoming progressively available because of their increased signal-to-noise ratio (SNR) and enhanced parallel imaging performance. However, longer reconstruction time and intensive computational cost have become significant concerns as the number of channels increases, especially in some iterative reconstructions. Coil compression can effectively solve this problem by linearly combining the raw data from multiple coils into fewer virtual coils. In this work, geometric-decomposition coil compression (GCC) is applied to radial sampling (both linear-angle and golden-angle patterns are discussed) for better compression. GCC, which is different from directly compressing in k-space, is performed separately in each spatial location along the fully sampled directions, then followed by an additional alignment step to guarantee the smoothness of the virtual coil sensitivities. Both numerical simulation data and in vivo data were tested. Experimental results demonstrated that the GCC algorithm can achieve higher SNR and lower normalized root mean squared error values than the conventional principal component analysis approach in radial acquisitions.