The precise speed and position control technique for Brushless DC Motor demands accurate position and speed feedback information. Generally, resolver or absolute encoders are used as speed and positiion sensor. But they increase cost and more problem happens at low speed than high speed specially. Therefore, in this paper, optimal speed observer is proposed for decreasing size and cost of whole system. And also, we consider the error problem about the system modeling and measurement at low speed range as well as high speed. The overall system consists of two parts, a drive and a speed observer. We make use of Least square curve fitting algorithm as speed observer and can overcome low resolution by proposed observer. Also, because of using the signal of hall sensor, robust control is possible in low speed as well as high speed for the change of the parameters of the system and disturbance. To construct observer using the signal of hall sensor, we design the pulse multiplier circuit and the software of microprocessor, AT89CC2051. Finally, the performance of the proposed observer is exemplified by some simulations and experiments.