Laparoscopic liver surgery, while minimally invasive, poses significant challenges in accurately identifying critical anatomical structures. Augmented reality (AR) systems, integrating MRI/CT with laparoscopic images based on 2D-3D registration, offer a promising solution for enhancing surgical navigation. A vital aspect of the registration progress is the precise detection of curvilinear anatomical landmarks in laparoscopic images. In this paper, we propose BCRNet (Bezier Curve Refinement Network), a novel framework that significantly enhances landmark detection in laparoscopic liver surgery primarily via the Bezier curve refinement strategy. The framework starts with a Multi-modal Feature Extraction (MFE) module designed to robustly capture semantic features. Then we propose Adaptive Curve Proposal Initialization (ACPI) to generate pixel-aligned Bezier curves and confidence scores for reliable initial proposals. Additionally, we design the Hierarchical Curve Refinement (HCR) mechanism to enhance these proposals iteratively through a multi-stage process, capturing fine-grained contextual details from multi-scale pixel-level features for precise Bezier curve adjustment. Extensive evaluations on the L3D and P2ILF datasets demonstrate that BCRNet outperforms state-of-the-art methods, achieving significant performance improvements. Our code is available at https://github.com/jinlab-imvr/BCRNet .