Accurate and safety-quantifiable localization is of great significance for safety-critical autonomous systems, such as unmanned ground vehicles (UGV) and unmanned aerial vehicles (UAV). The visual odometry-based method can provide accurate positioning in a short period but is subjected to drift over time. Moreover, the quantification of the safety of the localization solution (the error is bounded by a certain value) is still a challenge. To fill the gaps, this paper proposes a safety-quantifiable line feature-based visual localization method with a prior map. The visual-inertial odometry provides a high-frequency local pose estimation which serves as the initial guess for the visual localization. By obtaining a visual line feature pair association, a foot point-based constraint is proposed to construct the cost function between the 2D lines extracted from the real-time image and the 3D lines extracted from the high-precision prior 3D point cloud map. Moreover, a global navigation satellite systems (GNSS) receiver autonomous integrity monitoring (RAIM) inspired method is employed to quantify the safety of the derived localization solution. Among that, an outlier rejection (also well-known as fault detection and exclusion) strategy is employed via the weighted sum of squares residual with a Chi-squared probability distribution. A protection level (PL) scheme considering multiple outliers is derived and utilized to quantify the potential error bound of the localization solution in both position and rotation domains. The effectiveness of the proposed safety-quantifiable localization system is verified using the datasets collected in the UAV indoor and UGV outdoor environments.