Laboratory nanocomputed tomography (nano-CT), which can provide a spatial resolution of up to 100 nm, has been widely used due to its volume advantage. However, the drift of the x-ray source focal spot and the thermal expansion of the mechanical system can cause projection drift during long-time scanning. The three-dimensional result reconstructed from the drifted projections contains severe drift artifacts, which reduce the spatial resolution of nano-CT. Registering the drifted projections using rapidly acquired sparse projections is one of the mainstream correction methods, but the high noise and contrast differences of projections in nano-CT affect the correction effectiveness of existing methods. Herein, we propose a rough-to-refined projection registration method, which fully combines the information of the features in the gray and frequency domains of the projections. Simulation data show that the drift estimation accuracy of the proposed method is improved by 5× and 16× compared with the mainstream random sample consensus and locality preserving matching based on features. The proposed method can effectively improve the imaging quality of nano-CT.