Precise and robust extrinsic parameter calibration is fundamental for LiDAR-camera multi-modal sensing applications. However, most existing methods assume that sensors have the same orientation, limiting their effectiveness in feature extraction and feature alignment from different angle of view in multi-angle sensing scenarios. Moreover, the calibration accuracy of existing methods is insufficient for high-performance applications. To address these limitations, we propose a novel automatic extrinsic parameter calibration method utilizing a spherical target. We propose the Curvature Consistency Spherical Detection (CCSD) algorithm for LiDAR point cloud sphere recognition. The CCSD leverages the sphere's structural attributes, enabling robust detection against noise and partial occlusion. To improve camera sphere detection, we present an enhanced ellipse detection technique and compensate the eccentricity error arising from spherical projection based on the principle of perspective transformation. Extensive simulations and real-world experiments demonstrate the proposed method's superiority in accuracy and practicality over state-of-the-art (SOTA) methods.