A method of producing a copper alloy wire rod, containing: a casting step for obtaining an ingot by pouring molten copper of a precipitation strengthening copper alloy into a belt-&-wheel-type or twin-belt-type movable mold; and a rolling step for rolling the ingot obtained by the casting step, which steps are continuously performed, wherein an intermediate material of the copper alloy wire rod in the mid course of the rolling step or immediately after the rolling step is quenched.