A multichannel active noise control (ANC) method with exterior radiation suppression is proposed. When applying ANC in a three-dimensional space by using multiple microphones and loudspeakers, the loudspeaker output can amplify noise outside a region of target positions because most of current ANC methods do not take into consideration the exterior radiation of secondary loudspeakers. We propose a normalized least mean square algorithm for feedforward ANC in the frequency domain based on the Riemannian optimization to update the control filter with the exterior radiation power constrained to a target value. The advantages of the proposed method, compared with the algorithm using a penalty term of exterior radiation, were validated by numerical experiments: the exterior radiation power can be constrained during the adaptation process and the parameter for the constraint can be determined in advance.