In the detection of a point source with Hartmann wavefront sensor, besides the normal noise sources such as signal photon noise, readout noise and background noise, the blind pixels existing on the image sensor may also introduce centroid detection error. The integral formula of centroid detection error in the presence of a single blind pixel in the spot area is put forward. Furthermore, analysis about the two influence factors of centroid displacement error induced by single blind pixel, i.e., the distance between single blind pixel and spot center and the Gaussian width of the spot is presented. The simulation and experimental results are in accordance with the theoretical analysis.