The limit of detection (LOD) and range of quantitation (ROQ) of competitive enzyme-linked immunosorbent assay (ELISA) were determined from a model describing the calibration curve and precision profile of the assay. The calibration curve is given by solving the differential equations describing the change in the concentrations of an antigen-antibody complex and an enzyme-conjugated antigen-antibody complex by a Runge-Kutta method. The precision profile is described in terms of possible error sources such as the pipetting volumes of the analyte, enzyme-conjugated antigen, antibody and substrate solutions, calibration curve and inherent absorbances between the wells in an ELISA plate. An appropriate concentration of the enzyme-conjugated antigen that balances a low detection limit and sufficient color development was found to be in a narrow range, which is consistent with the empirical rule. The optimum conditions for competitive ELISA using an antibody with a kinetic property can be designed from our model.