A novel approach of a phase shifted all-optical analog-to-digital converter with double parallel intensity modulator is proposed and demonstrated. The phase shift of quantization curve is simply realized by optical attenuation. The proposed scheme can solve the problem of pulse walk-off, and low precision of phase shift in the present phase shifting quantization schemes as well as the influence of environment and temperature. In this scheme, the outputs of two parallel LiNbO3 intensity modulators are split into 4 channels with an optical attenuator inserted in each channel. By appropriately adjusting the optical attenuators, the phase shift between two adjacent channels is achieved, thus 8-channel optical quantizer is realized with resolution of 4 bits. In the experiment, a 10 GHz sinusoidal input signal is quantized using this scheme with an effective number of 3.7 bits. The deviation from the ideal case is only 0.3 bits. This result donates that the proposed approach is feasible, and has a relatively high effective number of bits compared with the present schemes.