This paper proposes a novel acceleration estimation method for motion control with a optical position encoder. It is well known that acceleration control is effective to construct a robust control system. Therefore, there are a lot of strong demands on efficient acceleration estimation method. Proposed estimation method is based on a least squares method. Least squares method applies to discrete position response versus time data taking the quantization error into consideration. The relation between the estimation delay and accuracy is discussed, and how to decide the number of samples is proposed. The validity of the proposed method is confirmed by simulation results.