Objective. In carbon ion therapy, the visualization of the range of incident particles in a patient body is important for treatment verification. In-beam positron emission tomography (PET) imaging is one of the methods to verify the treatment in ion therapy due to the high quality of PET images. We have shown the feasibility of in-beam PET imaging of radioactive 15O and 11C ion beams for range verification using our OpenPET system. Recently, we developed a whole gamma imager (WGI) that can simultaneously work as PET, single gamma ray and triple gamma ray imaging. The WGI has high potential to detect the location of 10C, which emits positrons with a simultaneous gamma ray of 718 keV, within the patient's body during ion therapy. Approach. In this work, we focus on investigating the performance of WGI for 10C imaging and its feasibility for range verification in carbon ion therapy. First, the performance of the WGI was studied to image a 10C point source using the Geant4 toolkit. Then, the feasibility of WGI was investigated for an irradiated polymethyl methacrylate (PMMA) phantom with a 10C ion beam at the carbon therapy facility of the Heavy Ion Medical Accelerator in Chiba. Main results. The average spatial resolution and sensitivity for the simulated 10C point source at the centre of the field of view were 5.5 mm FWHM and 0.010%, respectively. The depth dose of the 10C ion beam was measured, and the triple gamma image of 10C nuclides for an irradiated PMMA phantom was obtained by applying a simple back projection to the detected triple gammas. Significance. The shift between Bragg peak position and position of the peak of the triple gamma image in an irradiated PMMA phantom was 2.8 ± 0.8 mm, which demonstrates the capability of triple gamma imaging using WGI for range verification of 10C ion beams.