In grating based multi-contrast x-ray imaging, signals of three contrast mechanisms, namely absorption contrast, differential phase contrast (DPC) and dark-field contrast, can be estimated from a single data acquisition with several phase steps. The extracted signals, N0 (related to absorption), N1 (related to dark-field) and φ (related to DPC) may be intrinsically biased. In this work, the biases of the extracted N0, N1 and φ from the well-known least square fitting method were theoretically derived. Furthermore, numerical simulation experiments were used to validate the derived theoretical formulae for the signal bias of all three contrast mechanisms. The theoretical predictions were in good agreement with the results of the simulations. The bias of the absorption contrast is zero. The signal bias for N1 is inversely proportional to the number of phase steps and to the average fringe visibility of the grating interferometer. The bias of φ is related to several parameters, including the total exposure, the fringe visibility produced by the interferometer system, and the ground truth of φ. The larger the exposure and fringe visibility, the smaller the bias of φ.