The numerical investigation of two main factors, velocity shear and wall proximity effect, which affects mean velocity measurement for low Reynolds number wall-bounded flow using Pitot tubes, was carried out. Their effects were separated through careful numerical simulation and cases were run for each of them respectively for error analysis. The simulation results show that: for velocity shear, the result of current work basically agrees with that of related literature, however, the nondimensional streamline shift does not asymptotically approach to a constant value; noticeable wall vicinity effect can be found within 5 tube diameters to the wall, and errors are decreasing within 1 tube diameter to the wall. Comparisons were made among the numerical solutions in this work and the corrections being used in the literature, and the new corrections based on simulation results of current work were given in the end.