Objective: With the rapid development of vehicular networks (vehicle-to-everything) and autonomous driving technologies, cooperative perception has become a crucial technology to enhance the environmental perception capability of connected and autonomous vehicles (CAVs). Individual perception information is shared among CAVs, and cooperative perception can effectively expand the sensing range, reduce occlusion effects, and improve perception redundancy. However, vehicle localization errors are unavoidable in real driving scenarios due to sensor noise, environmental interference, and communication uncertainty. Localization errors often lead to spatial misalignment among point clouds from multiple vehicles, thereby reducing the performance of multivehicle cooperative perception. Mitigating the impact of localization errors on cooperative perception and improving computational efficiency for on-board deployment remain challenging problems. Methods: To address the above issues, this paper proposed a cooperative perception method of CAVs based on point feature fine alignment. First, a lightweight point feature extraction module was designed using PointConvFormer to process point cloud data collected by individual vehicles. By integrating PointConvFormer layers into bottleneck residual blocks, the proposed feature extraction module preserves the three-dimensional spatial structure of the point cloud while capturing local geometric features and global contextual information. Second, the cross-vehicle point feature hierarchical fine alignment module was designed to address spatial misalignment in cross-vehicle data fusion. This module used the global poses of multiple CAVs, collected from positioning systems, to achieve coarse alignment of point features between the surrounding CAVs and the ego-vehicle. The fine-grained alignment strategy was further implemented using local overlapping point-cloud registration to improve the spatial feature consistency of the aggregated point cloud, and the point feature similarity within overlapping regions was exploited to maximize cross-vehicle feature correspondence and alleviate feature alignment deviation caused by localization errors. Furthermore, the multiscale feature fusion module was built to integrate local fine-grained features with global contextual information; it employed multiscale mask sampling to retain the structural information of the aligned aggregated point cloud at various spatial resolutions. Results: Extensive experiments and ablation studies were conducted on V2V4real and V2XSet datasets to comprehensively evaluate the performance of the proposed method. The experimental results demonstrated that the proposed approach achieved superior perception accuracy and robustness compared to other state-of-the-art methods across traffic scenarios with varying levels of localization errors. Moreover, the proposed method maintained high computational efficiency and satisfied the real-time requirements of on-board deployment. Conclusions: The proposed cooperative perception method, based on point feature fine alignment, integrates a lightweight point feature extraction module, a cross-vehicle point feature fine alignment module, and a multiscale feature fusion module. It effectively addressed the perception performance degradation problem caused by vehicle localization errors and improved the accuracy and robustness of cooperative perception among CAVs. In future work, we will enhance the collaborative perception performance of CAVs in complex scenarios, such as rain and fog, by integrating information from multimodal sensors, including cameras and millimeter-wave radars.