Process for conversion of a paraffinic feedstock that has a number of carbon atoms of between 9 and 25, whereby said paraffinic feedstock is produced starting from renewable resources, excluding paraffinic feedstocks that are obtained by a process that involves a stage for upgrading by the Fischer-Tropsch method, whereby said process uses a catalyst that comprises at least one hydrogenating-dehydrogenating metal that is selected from the group that is formed by the metals of group VIB and group VIII of the periodic table, taken by themselves or in a mixture, and a substrate comprising at least one IZM-2 zeolite and at least one binder, whereby said process is carried out at a temperature of between 150 and 500° C., at a pressure of between 0.1 MPa and 15 MPa, at an hourly volumetric flow rate of between 0.1 and 10 h−1, and in the presence of a total quantity of hydrogen that is mixed with the feedstock such that the hydrogen/feedstock ratio is between 70 and 2,000 Nm3/m3 of feedstock.