Due to various advantages of Wheeled Mobile Robots (WMRs), many researchers have focused to solve their challenges. The automatic motion control of such robots is an attractive problem and is one of the issues which should carefully be examined. In the current paper, the trajectory tracking problem of WMRs which are actuated by two independent electrical motors is deliberated. To this end, and also, computer simulation of the system, first the system model is derived at the level of kinematics. The system model is nonholonomic. Then a simple non-mode-based controller based on fuzzy logic will be proposed. The control input resulted from fuzzy logic will then be corrected to fulfill the actuation saturation limits and non-slipping condition. To prove the efficiency of the suggested controller, its response, in terms of the required computational time burden and tracking error, will be compared with a previously suggested method. The obtained simulation results support the superiority of fuzzy based method over a previous study in terms of the considered measures.