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This paper presents mathematical modeling and simulation results of a wheelchair system with motion control, which constitutes a crucial part of a research project on vision-based smart wheelchair control and navigation. Disabled people with neuromuscular or reflex disabilities have difficulties in operating standard electric wheelchairs properly. In addition to, driving wheelchair in outdoor has critical risks. The work will contribute greatly mobility problem of disabled people by visual information technology and efficient motion control design simulation. To reach this purpose, the mathematical model of wheelchair is constructed that shows main characteristics and dynamical behavior of system. Results of the study is observed by a designed computer simulation model. Simulation test outcomes provide developing control algorithm that well organized motor control. Computer simulation results include controlling the position and direction of wheelchair, linear displacement, velocity information and disturbance effect on driving. Consequencely, the mathematical model has the ability to show the representing autonomous wheelchair dynamics in open-loop and closed-loop and simulation outputs prove effeciency of the model and designed control system. Results of the study will be used in the research project that aims to solve the autonomous wheelchair control problem.