This paper proposes a super twisting sliding mode control for a bidirectional dual active bridge (DAB) converter. First of all, the mathematical model of the DAB converter developed around the Fourier expansion of the switching functions is defined and then a super twisting sliding function is proposed to regulate the output voltage while utilizing a sliding mode observer to estimate the load disturbance to get a feedforward term to the control input. On the contrary of the classical sliding mode control methods, the proposed sliding function is capable of alleviating the chattering while attaining zero steady state error and finite time convergence by estimating the load current and feedforwarding to the control loop. Since the control input is smooth, it can be directly injected to the PWM block for generating switching signals that cause fixed switching frequency. The effectiveness of the proposed method is verified in the MATLAB/ simulation software. The results confirm the disturbance rejection, fast response, and chattering alleviation of the proposed strategy thanks to the inherent characteristics of the super twisting method.