This paper describes an adaptive model free speed control algorithm for DC motors, based on a recursive least-squares with forgetting factor. In order to control the speed of a DC motor, only the factors of output speed and voltage values have been used without a mathematical model of the DC motor. As the relationship between the input voltage and the DC motor speed in a specific region can be approximated as a first order system, the coefficient that represents the approximated first order system has been estimated by using a recursive least-squares approach with a forgetting factor model. Also, the error between the actual system and the approximated first order system has been estimated by a disturbance observer. Based on the estimated coefficient of the first order system, as well as this disturbance, an optimal input for tracking the desired velocity has been computed by using the Lyapunov direct method. Weighting factor adaptation rules have been proposed to enhance control performance. This performance evaluation has been conducted in a MATLAB/Simulink environment using a DC motor dynamic model for realistic evaluation. The evaluation results show that the developed adaptive DC motor speed control method ensures good tracking performance by using only the input voltage and the output speed information.