A first hydroisomerization catalyst contains a support being a extruded product prepared by calcination having a thermal treatment that includes thermally treating at 350° C. or more and at least one metal supported on the support and selected from the group consisting of metals belonging to Groups 8 to 10 of the periodic table, molybdenum and tungsten, wherein the support contains (a1) a calcined zeolite prepared by calcination having a thermal treatment that includes thermally treating at 350° C. or more of an ion-exchanged zeolite obtained by ion exchange of an organic template-containing zeolite containing an organic template and having a 10-membered ring one-dimensional porous structure in a solution containing ammonium ions and/or protons, and (b1) a calcined inorganic oxide prepared by calcination having a thermal treatment that includes thermally treating at 350° C. or more of one inorganic oxide selected from the group consisting of alumina, silica, titania, boria, zirconia, magnesia, ceria, zinc oxide, phosphorus oxide, and a composite oxide containing a combination of two or more of these oxides, wherein the thermal treatment to which the calcined zeolite has been subjected includes calcination in which the ion-exchanged zeolite that has not been thermally treated at 350° C. or more is heated within the range of 350° C. to 450° C.