Digital phase shifters are widely used to achieve space scanning in phased array antenna, and beam pointing accuracy depends on the bit number and resolution of the digital phase shifter. This paper proposes a novel phase feeding method to reduce the phase quantization error effects. A linear formula for the beam pointing deviation of a linear uniform array in condition of phase quantization error is derived, and the linear programming algorithm is introduced to achieve the minimum beam pointing deviation. Simulations are based on the pattern of the phased array, which gives each element a certain quantization phase error to find the beam pointing deviation. The novel method is then compared with previous methods. Examples show that a 32-element uniform linear array with 5-bit phase shifters using the proposed method can achieve a higher beam-steering accuracy than the same array with 11-bit phase shifters.