An advantage of heavy-ion therapy is its good dose concentration. A limit for full use of this desirable feature comes from range ambiguities in treatment planning. The treatment planning is based on X-ray CT measurements, and the range ambiguities are mainly due to an error in calibration of the CT number. The heavy-ion ranges are related to electron density of the medium while the CT numbers are defined using the X-ray attenuation coefficient. The range verification method using positron emitter beams has been developed to reduce the range ambiguities. In this verification, probing beams of positron emitters are implanted into the tumor, and pairs of annihilation gamma rays are detected with a positron camera. This paper demonstrates an application to verify treatment planning. Here the treatment planning was made on a head phantom and the ranges estimated from the CT-number were compared with the ranges measured with the positron camera. As a result, disagreements were detected between the planned ranges and the measured ones; there were 1.6 mm at maximum. The disagreements were due to an error of transformation of CT-number to range for the phantom material in the water column depth-dose measurement. The disagreements could be lowered to 0.4 mm by using the calibrated water-equivalent lengths. It was confirmed that the range verification system has a designed measurement accuracy of 1 mm and is useful for verifying irradiation fields on heavy-ion radiotherapy.