The precise dose distribution fitted with a tumor shape in a beam direction tend to be more fragile if the beam's eye view (BEV) of the three dimensional (3D) electron density (ED) map in the beam direction changed more abruptly (high frequency) with large variation (large amplitude). This could lead to significant tumor underdose, but fatal overdose in organs at risk. In this study, we developed an automated method for determination of robust beam directions against the patient setup error based on the ED-based BEV in the beam direction in the particle therapy. The basic idea of our approach was to find the robust beam directions, whose ED- based BEV has low special frequency variation with small amplitude. For evaluation of the variation in the ED-based BEV in a beam direction, we calculated power spectra of the ED-based BEVs in all directions (0 to 355 degree) with an interval of 5 degree. We assume that as the spatial frequency and amplitude of the variation in the ED-based BEV in a beam direction is lower and smaller, respectively, the gradient of the power spectrum becomes larger, which means the robust beam direction. The ED-based BEV was produced by projection of a 3D electron density map derived from the computed tomogra- phy (CT) image from a beam source to a planning target volume (PTV) distal end. The gradient of the power spectrum was obtained as the slope of a one-order polynomial with the power spectral values for all frequencies until a Nyquist frequency.The proposed methodology was applied to four head and neck cancer patients for determination of robust beam directions. As a preliminary result, radiation oncologists agreed with most beam directions, which seem to be robust against patient setup errors, suggested by the proposed method.