In terms of the application of the ion sensitive field effect transistor (ISFET) fabricated with top-down approached and CMOS-compatible back-end process to integrated circuits, the macro model of the ISFET is required. Although several models have been reported, there is no electrical model that reflects the time-dependent drain current (ID) change (drift effect). We propose the electrical model which can reflect the drift effect and can be expressed by the combination of electrical circuit components. In the proposed model, R1 represents the resistance of the electrolyte and the FET can be approximated by the capacitances C1 (capacitance of pure gate oxide in which hydrogen ions move very slowly) and C2 (capacitance by gate oxide with defects in which hydrogen ions move relatively faster). Furthermore, the movement of hydrogen ions in the defective oxide is represented by R2 and the current drift is modeled as the parallel combination of the C2 and the R2 because the drift effect is strongly related to hydrogen ion movement through defective gate oxide or Helmholtz layer. Consequently, the ISFET with the ID drift can be modeled by the series connection of the R1, the parallel combination of the C2 and the R2, and the C1. Also, The ID calculated by the proposed model is successfully fitted to the measured time-dependent ID of the ISFET.