PURPOSE: To perform high accurate control in no relation to unevenness and aged deterioration of parts in the feedback control method of air-fuel ratio, by correcting supply of fuel with study quantities in accordance with a corrective amount of air-fuel ratio in a low prescribed range and in a high range.

CONSTITUTION: When a basic fuel injection amount TP is corrected by study quantitites GAK1, 2, a hyperbolic function with an NTP as a variable is used for a corrective coefficient, and the coefficient is set corresponding to GAK1/ NPT+GAK2. An error of the injection amount TP obtained from a two-dimensional map by unevenness, aged deterioration, etc. of constitutional parts in each engine is such that the error is rapidly increased, if the NTP becomes small, in an idle range of C10WC11 normally with the small NTP of a small amount of intake air while the error is in a fixed level in a range of C20W C21 with the large NTP of large amount of intake. Accordingly, if study control is performed with the GAK1 studied in the range of C10WC11 as the slope of a hyperbolic function of the NTP while with the GAK2 studied in the range of C20WC21 as the offset amount, the error of the TP can be reduced.