This simulation study presents the application of fluence field modulated computed tomography, initially developed for x-ray CT, to proton computed tomography (pCT). By using pencil beam (PB) scanning, fluence modulated pCT (FMpCT) may achieve variable image quality in a pCT image and imaging dose reduction. Three virtual phantoms, a uniform cylinder and two patients, were studied using Monte Carlo simulations of an ideal list-mode pCT scanner. Regions of interest (ROI) were selected for high image quality and only PBs intercepting them preserved full fluence (FF). Image quality was investigated in terms of accuracy (mean) and noise (standard deviation) of the reconstructed proton relative stopping power compared to reference values. Dose calculation accuracy on FMpCT images was evaluated in terms of dose volume histograms (DVH), range difference (RD) for beam-eye-view (BEV) dose profiles and gamma evaluation. Pseudo FMpCT scans were created from broad beam experimental data acquired with a list-mode pCT prototype. FMpCT noise in ROIs was equivalent to FF images and accuracy better than -1.3%(-0.7%) by using 1% of FF for the cylinder (patients). Integral imaging dose reduction of 37% and 56% was achieved for the two patients for that level of modulation. Corresponding DVHs from proton dose calculation on FMpCT images agreed to those from reference images and 96% of BEV profiles had RD below 2 mm, compared to only 1% for uniform 1% of FF. Gamma pass rates (2%, 2 mm) were 98% for FMpCT while for uniform 1% of FF they were as low as 59%. Applying FMpCT to preliminary experimental data showed that low noise levels and accuracy could be preserved in a ROI, down to 30% modulation. We have shown, using both virtual and experimental pCT scans, that FMpCT is potentially feasible and may allow a means of imaging dose reduction for a pCT scanner operating in PB scanning mode. This may be of particular importance to proton therapy given the low integral dose found outside the target.