Image registration is of great clinical importance in computer aided diagnosis and surgical planning of liver diseases. Deep learning-based registration methods endow liver computed tomography (CT) image registration with characteristics of real-time and high accuracy. However, existing methods in registering images with large displacement and deformation are faced with the challenge of the texture information variation of the registered image, resulting in subsequent erroneous image processing and clinical diagnosis. To this end, a novel unsupervised registration method based on the texture filtering is proposed in this paper to realize liver CT image registration. Firstly, the texture filtering algorithm based on L0 gradient minimization eliminates the texture information of liver surface in CT images, so that the registration process can only refer to the spatial structure information of two images for registration, thus solving the problem of texture variation. Then, we adopt the cascaded network to register images with large displacement and large deformation, and progressively align the fixed image with the moving one in the spatial structure. In addition, a new registration metric, the histogram correlation coefficient, is proposed to measure the degree of texture variation after registration. Experimental results show that our proposed method achieves high registration accuracy, effectively solves the problem of texture variation in the cascaded network, and improves the registration performance in terms of spatial structure correspondence and anti-folding capability. Therefore, our method helps to improve the performance of medical image registration, and make the registration safely and reliably applied in the computer-aided diagnosis and surgical planning of liver diseases.