In this research, a snake-like robot with flexible connectors is developed, and an optimal velocity planning approach is investigated under the constraints of path, kinematics and dynamics of the robot. The snake-like robot includes five modules which are connected by flexible connectors; each module is driven by two stepping motors and is controlled in differential way for its direction and speed by micro-controllers. Flexible connection makes the motion of the robot smoother and more snake-like. However, the elastic restoring force and torque due to longitudinal extension (or compression) and lateral bending of springs may affect the behavior of the snake-like robot during moving. The snake-like robot will be out of control unless proper planning. The snake-like robot is capable of following the planned path and arriving at the destination in minimum time without sliding or losing steps, if the optimal velocity planned by the study is applied.