The main purpose of this study is to construct a system to track the tumor position during radiofrequency ablation (RFA) treatment. Existing tumor tracking systems are designed to track a tumor in a two-dimensional (2D) ultrasound (US) image. As a result, the three-dimensional (3D) motion of the organs cannot be accommodated and the ablation area may be lost. In this study, we propose a method for estimating the 3D movement of the liver as a preliminary system for tumor tracking. Additionally, in current 3D movement estimation systems, the motion of different structures during RFA could reduce the tumor visibility in US images. Therefore, we also aim to improve the estimation of the 3D movement of the liver by improving the liver segmentation. We propose a novel approach to estimate the relative 6-axial movement (x, y, z, roll, pitch, and yaw) between the liver and the US probe in order to estimate the overall movement of the liver. We used a convolutional neural network (CNN) to estimate the 3D displacement from two-dimensional US images. In addition, to improve the accuracy of the estimation, we introduced a segmentation map of the liver region as the input for the regression network. Specifically, we improved the extraction accuracy of the liver region by using a bi-directional convolutional LSTM U-Net with densely connected convolutions (BCDU-Net). By using BCDU-Net, the accuracy of the segmentation was dramatically improved, and as a result, the accuracy of the movement estimation was also improved. The mean absolute error for the out-of-plane direction was 0.0645mm/frame. The experimental results show the effectiveness of our novel method to identify the movement of the liver by BCDU-Net and CNN. Precise segmentation of the liver by BCDU-Net also contributes to enhancing the performance of the liver movement estimation.