Steering accuracy is limited by the quantized phase modulation values and the number of phase pixels for spatial light modulators (SLMs). Conventional methods of beam steering lack optimum precision. In this letter, a beam steering approach based on horizontally moving phase steps is proposed. Compared with the conventional methods, this novel method is able to reduce the maximum normalized steering error in SLM significantly by a factor proportional to the number of pixels. In addition, steering errors of high steering angles can be drastically reduced by a factor proportional to the product of the number of pixels and the quantized phase levels; the number of high-precision steering angles increases with the number of pixels or the quantized phase levels increasing.