Disclosed is an ironing apparatus for a hat. The ironing apparatus for a hat includes: a hollow spherical conductor having an opening formed at a lower portion thereof; supports installed under the spherical conductor to support the spherical conductor with being spaced apart from a bottom plate; and a hot air supplier installed under the opening formed at the lower portion of the spherical conductor to vertically supply hot air to an inner space of the spherical conductor. According to the present invention, it is possible to rapidly and economically ironing the hat, thereby improving a commercial value of the hat. Further, according to the present invention, it is possible for a user to freely use his/her two hands while adjusting heat required for ironing by using his/her foot during ironing the hat, thereby improving ironing quality of the hat.