The Brownian motion in a harmonic trap is studied by magnetic tweezers experiment and computer simulation. The results of the experiment and simulation validate the theory. Then the theory is used to analyze the experimental results including the effect of persistent length of DNA on the displacement distribution of the bead and the error in force measurements. It can be concluded that the variation of the persistent length affects more the Brownian motion along the DNA chain than in the other direction; under a small force, a considerable error of the force measurement will occur.