Radar target detection on the sea surface is challenging due to the influence of sea clutter. Traditional radar target detection methods cannot model the sea clutter distributions precisely, resulting in poor target detection performance. In this letter, we propose a novel PointNet-based method to parallelly detect multiple targets. We extract the global features to solve a classification problem, that is, detecting whether there exist the targets in a radar echo frame, and extract the local features to solve a segmentation problem, that is, detecting whether it has a target in each range cell. In addition, to implement constant false alarm rate (CFAR) detection, we apply a statistical method by precisely adjusting the detection threshold to keep a desired probability of false alarm (PFA). Simulation results show that the proposed method can realize the target classification with a 95.985% total accuracy rate when the PFA is 0.1 and achieve a larger detection probability under a desired PFA based on the IPIX radar dataset compared with the baselines.