The invention relates to a continuous process for pretreatment of an oil feedstock comprising at most 20% by weight of free fatty acids by esterification of free fatty acids in which a vertical liquid/liquid contactor containing an esterification catalyst in solid form is supplied in counter-current by an alcohol feedstock comprising at least 20% by weight of an alcohol and said oil feedstock, with said contactor being operated at a temperature of between 25 and 120° C., with said contactor performing the contact in liquid-liquid counter-current between a heavy phase and a light phase, with said heavy phase being able to be either an oil-rich phase or an alcohol-rich phase.