This paper presents algorithms for three-dimensional tracking of surgical needles using the stereo endoscopic camera images obtained from the da Vinci Surgical Robotic System. The proposed method employs Bayesian state estimation, computer vision techniques, and robot kinematics. A virtual needle rendering procedure is implemented to create simulated images of the surgical needle under the da Vinci robot endoscope, which makes it possible to measure the similarity between the rendered needle image and the real needle. A particle filter algorithm using the mentioned techniques is then used for tracking the surgical needle. The performance of the tracking is experimentally evaluated using an actual da Vinci surgical robotic system and quantitatively validated in a ROS/Gazebo simulation thereof.