Hopping robots are kind of legged robot that have better mobility in a natural environment in comparison with wheeled robots. Their motion style is in two phases of stance and flight which are repeated alternatively. They can move with great speed and maneuverability even on rough terrain. A great capability in evading obstacles indicates that the hopping robots may be suitable for reconnaissance tasks. The dynamic balance and special motion style of the hopping robots can provide a fundamental research bed for walking robots or running robots. The simple mechanical construction of a one-legged robot also provides a perfect test bed for studying control of mechanical systems. The hopping robots holds many researchers interests in recent years because working on these robots is almost simple and that result could be used for designing complicated robots with more than one leg like humanoid and biologically-iired robots. In this research, dynamic analysis and control of a one-legged hopping robot is survived. In this regard, a model of a planar one-legged hopping robot with two actuators is considered and then the suitable dynamical model using Lagrange method is obtained and finally the mentioned model is simulated in matlab software. To create a stable motion and correctly traort from flight phase to stance phase and vice versa, robot motion in both phases is survived and suitable planning to achieve to a desired condition is done. Then according to recent planning, the robot’s behavior in each phases is controlled. First of all using common control methods like PD and computed torque, the motion of the robot is controlled. Using correct planning of these controllers, the robot is able to achieve the goals in a stable motion. Continually the mentioned controller performance in a way that the measured parameters by sensors with noise, was used and was observed that this controller was not able to counter with noise and the robot couldn’t follow the desired trajectories, therefore FMRLC control method as a kind of adaptive fuzzy controller was introduced and applied on the robot. This method has a learning mechanism which makes it able to modify the fuzzy controller rules during the time, therefore using FMRLC method and several repeating of desired trajectory, the controller was learned and robot motion in desired trajectory was improved during time. Keywords: Hopping robot, One-legged robot, Flight phase, Stance phase, Lagrange method, Fuzzy control, FMRLC