This paper studies leader-follower formation control of networked nonholonomic vehicles of unicycle type. Each vehicle is subject to the velocity constraints consisting of saturated angular velocity and bounded linear velocity with positive-minimum value. Each vehicle is allowed to use its local coordinate frame, and the network topology is described by a directed graph containing a spanning tree. Two dynamic control laws satisfying the velocity constraints are developed respectively, such that the leader-follower formation defined in local coordinate frames can be achieved in two cases. The proposed control laws only require each vehicle to use the information of its neighbors in the network via local measurements and communication. Finally,effectiveness is illustrated by simulation results of an example. This paper studies leader-follower formation control of networked nonholonomic vehicles of unicycle type. Each vehicle is subject to the velocity constraint consisting of saturated angular velocity and bounded linear velocity with positive-minimum value. Each vehicle is allowed to use its local coordinate frame, and the network topology is described by a directed graph containing a spanning tree. The proposed control laws satisfying the velocity constraints are developed respectively, such that the leader-follower formation defined in local coordinate frames can be achieved in two cases. only require each vehicle to use the information of its neighbors in the network via local measurements and communication. Finally, effectiveness is illustrated by simulation results of an example.