Brain-computer interface (BCI) for robotic arm control has been studied to improve the life quality of people with severe motor disabilities. There are still challenges for robotic arm control in accomplishing a complex task with a series of actions. An efficient switch and a timely cancel command are helpful in the application of robotic arm. Based on the above, we proposed an asynchronous hybrid BCI in this study. The basic control of a robotic arm with six degrees of freedom was a steady-state visual evoked potential (SSVEP) based BCI with fifteen target classes. We designed an EOG-based switch which used a triple blink to either activate or deactivate the flash of SSVEP-based BCI. Stopping flash in the idle state can help to reduce visual fatigue and false activation rate (FAR). Additionally, users were allowed to cancel the current command simply by a wink in the feedback phase to avoid executing the incorrect command. Fifteen subjects participated and completed the experiments. The cue-based experiment obtained an average accuracy of 92.09%, and the information transfer rates (ITR) resulted in 35.98 bits/min. The mean FAR of the switch was 0.01/min. Furthermore, all subjects succeeded in asynchronously operating the robotic arm to grasp, lift, and move a target object from the initial position to a specific location. The results indicated the feasibility of the combination of EOG and SSVEP signals and the flexibility of EOG signal in BCI to complete a complicated task of robotic arm control.