Effects of direct and alternating current electric fields on the chemical oscillator have been investigated. The chemical oscillator was realized by immersing the cation exchange bead loaded with the ferroin catalyst in the Belousov-Zabotinsky reaction solution. Various dynamic behaviors appeared depending on the direction, the frequency, and the strength of the electric field. Their time series were characterized in terms of power spectra. Observed behaviors were explained by assuming a field-induced transport of the inhibitor Br-. A phase diagram concerning dynamic behaviors was obtained as a function of the frequency and the strength of the electric field. The irregular oscillation was found to necessarily appear in the transition between 1/1 and 1/2 (or 2/1) entrainments. For further examination, a three-dimensional phase portrait was constructed using the time-delay method, and the largest Lyapunov exponent was calculated.