A time optimal control method for quadruped walking robots is developed and installed into a practical robot system. The fastest straight walking has already been obtained by our previous study. Though that is only straight walking, moving range is restricted. Therefore, the purpose of this study is theory construction of curved walking for quadruped robots because of increasing moving range and earlier arriving at target. By means of deriving curved path stroke of robot body, placing position of legs, and dynamic equation of robot body, we obtain it.