This paper contributes to the fabrication of a snake-like robot in which the motion can be achieved through active wheels. The robot is constructed in such a way that its size can be increased and decreased, as well as it can undulate into a sine wave-like shape. The snake robot with wheels consists of chain of links attached to each other with the help of the passive prismatic and revolute joints. A neural oscillator-based central pattern generator (CPG) algorithm is applied to the robot so that rhythmic serpentine as well as rectilinear motions can be generated in it. In addition, a novel smooth transition mechanics of robot motion, from stationary position to serpentine or rectilinear motion as well as transition between these two gaits, is also suggested in the paper. The working of the formulated CPG motion algorithm is realized through experimental setup equipped with a motion capture system as well as through simulations.