A particle beam irradiation apparatus comprising: - an accelerator; - a scanning electromagnet; and - a scanning controller adapted to control the scanning electromagnet to irradiate a charged particle beam from the accelerator to an irradiation subject, - the scanning electromagnet having: an X-direction scanning electromagnet; and a Y-direction scanning electromagnet adapted to scan in a direction perpendicular to a scanning direction of the X-direction scanning electromagnet, - the scanning controller having: an X-direction inverse mapping mathematical expression model for generating an X-direction command value; and a Y-direction inverse mapping mathematical expression model for generating a Y-direction command value, from a desired irradiation position coordinate of the charged particle beam in the irradiation subject so that irradiation to the irradiation subject is implemented on the basis of the command values concerned, - wherein the X-direction and Y-direction scanning electromagnets (3a, 3b) are adapted to be controlled on the basis of the X-direction and Y-direction command values, respectively, generated from the desired irradiation position coordinate of the charged particle beam in the irradiation subject by the X-direction and Y-direction inverse mapping mathematical expression models, thereby irradiating the irradiation subject with the charged particle beam while scanning the charged particle beam, characterized in that: - each of the X-direction and Y-direction inverse mapping mathematical expression models are dependent upon two variables associated with the desired irradiation position coordinate on an irradiation position plane of the charged particle beam, wherein the two variables are the desired irradiation position coordinates in the specific scanning direction and in the direction perpendicular to it, and wherein each of the X-direction and Y-direction inverse mapping mathematical expression models is a polynomial expression. - an accelerator; - a scanning electromagnet; and - a scanning controller adapted to control the scanning electromagnet to irradiate a charged particle beam from the accelerator to an irradiation subject, - the scanning electromagnet having: an X-direction scanning electromagnet; and a Y-direction scanning electromagnet adapted to scan in a direction perpendicular to a scanning direction of the X-direction scanning electromagnet, - the scanning controller having: an X-direction inverse mapping mathematical expression model for generating an X-direction command value; and a Y-direction inverse mapping mathematical expression model for generating a Y-direction command value, from a desired irradiation position coordinate of the charged particle beam in the irradiation subject so that irradiation to the irradiation subject is implemented on the basis of the command values concerned, - wherein the X-direction and Y-direction scanning electromagnets (3a, 3b) are adapted to be controlled on the basis of the X-direction and Y-direction command values, respectively, generated from the desired irradiation position coordinate of the charged particle beam in the irradiation subject by the X-direction and Y-direction inverse mapping mathematical expression models, thereby irradiating the irradiation subject with the charged particle beam while scanning the charged particle beam, - each of the X-direction and Y-direction inverse mapping mathematical expression models are dependent upon two variables associated with the desired irradiation position coordinate on an irradiation position plane of the charged particle beam, wherein the two variables are the desired irradiation position coordinates in the specific scanning direction and in the direction perpendicular to it, and