The beam quality (M2) factor measurement requires the collimation of the optical path and the reduction of the influence of noise on the measurement of spot radius. Deviation of the optical path results in the deviation of the captured spot from the center of CCD, and the measurement values of spot radius and M2 factor will have extra error caused by noise. Aiming at the condition of containing noise and optical path deviating from the center of CCD, a modified method for M2 factor measurement is proposed. The proposed method can collect two spots at positions in optical path with different offsets when the optical path is not straight. The true value of spot radius can be obtained correctly, and then the M2 factor without collimation error can be obtained. The relationship among the spot radius of laser beam, the M2 factor and offset is deduced theoretically. Numerical simulation and experiments are carried out to study the relationship among the spot radius, M2 factor and offset. Consistent results are obtained, which proves the reliability of the proposed method.