This paper presents 3D vector flow images obtained using the 3D Transverse Oscillation (TO) method. The method employs a 2D transducer and estimates the three velocity components simultaneously, which is important for visualizing complex flow patterns. Data are acquired using the experimental ultrasound scanner SARUS on a flow-rig system with steady flow. The vessel of the flow-rig is centered at a depth of 30 mm, and the flow has an expected 2D circular-symmetric parabolic profile with a peak velocity of 1 m/s. Ten frames of 3D vector flow images are acquired in a cross-sectional plane orthogonal to the center axis of the vessel, which coincides with the y-axis and the flow direction. Hence, only out-of-plane motion is expected. This motion cannot be measured by typical commercial scanners employing 1D arrays. Each frame consists of 16 flow lines steered from -15 to 15 degrees in steps of 2 degrees in the ZX-plane. For the center line, 3200 M-mode lines are acquired yielding 100 velocity profiles. At the center of the vessel, the mean and standard deviation of the estimated velocity vectors are (vx, vy, vz) = (-0.026, 95, 1.0)±(8.8, 6.2, 0.84) cm/s compared to the expected (0.0, 96, 0.0) cm/s. Relative to the velocity magnitude this yields standard deviations of (9.1, 6.4, 0.88) %, respectively. Volumetric flow rates were estimated for all ten frames yielding 57.9±2.0 mL/s in comparison with 56.2 mL/s measured by a commercial magnetic flow meter. One frame of the obtained 3D vector flow data is presented and visualized using three alternative approaches. Practically no in-plane motion (vx and vz) is measured, whereas the out-of-plane motion (vy) and the velocity magnitude exhibit the expected 2D circular-symmetric parabolic shape. It shown that the ultrasound method is suitable for real-time data acquisition as opposed to magnetic resonance imaging (MRI). The results demonstrate that the 3D TO method is capable of performing 3D vector flow imaging.