In the context of COVID-19, the research on various aspects of the venipuncture robot field has become increasingly hot, but there has been little research on robotic needle insertion angles, primarily performed at a rough angle. This will increase the rate of puncture failure. Furthermore, there is sometimes significant pain due to the patients’ differences. This paper investigates the optimal needle entry angle decision for a dorsal hand intravenous injection robot. The dorsal plane of the hand was obtained by a linear structured light scan, which was used as a basis for calculating the needle entry angle. Simulation experiments were also designed to determine the optimal needle entry angle. Firstly, the linear structured optical system was calibrated and optimized, and the error function was constructed and solved iteratively by the optimization method to eliminate measurement error. Besides, the dorsal hand was scanned to obtain the spatial point clouds of the needle entry area, and the least squares method was used to fit it to obtain the dorsal hand plane. Then, the needle entry angle was calculated based on the needle entry area plane. Finally, the changes in the penetration force under different needle entry angles were analyzed to determine the optimal needle insertion angle. According to the experimental results, the average error of the optimized structured light plane position was about 0.1 mm, which meets the needs of the project, and a large angle should be properly selected for needle insertion during the intravenous injection.