Control method for coast stop vehicle

A coast stop vehicle, includes an engine (1), a transmission (4) arranged between the engine (1) and drive wheels (7) and having a plurality of gear positions, a coast stop starting unit which automatically stops the engine (1) when a coast stop start condition holds during travel, a coast stop releasing unit which automatically starts the engine (1) when a coast stop release condition holds during a coast stop, and a downshifting unit which starts engagement of a frictional engagement element (32), which realizes a lower gear position than the one when the coast stop release condition holds, before complete explosion of the engine (1) and causes a downshift of the transmission (4) when the coast stop release condition holds.