In this paper, a novel hardware-efficient central pattern generator (CPG) model based on asynchronous coupling of cellular automaton (CA) phase oscillators for a hexapod robot is presented. It is shown that the presented model can exhibit various synchronization patterns depending on parameter values. In order to analyze the synchronization patterns, a phase equilibrium and an evaluation function for a target synchronization pattern are introduced. As a result of the analysis, it is shown that an asynchronously coupled CA phase oscillators is suitable for the hexapod robot than a synchronously coupled CA phase oscillators. The presented asynchronous CPG model with parameters tuned appropriately is implemented on a field programmable gate array (FPGA) device and the device is mounted on a hexapod robot. A laboratory experiment verifies that the hexapod robot can reproduce one of typical gaits of six-legged insects. Finally, it is shown that the presented CPG model consumes far fewer circuits elements and much less power compared with one of conventional numerical integration CPG model and our previous CPG model.