Although proton therapy delivered using scanned pencil beams has the potential to produce better dose conformity than conventional radiotherapy, the created dose distributions are more sensitive to anatomical changes and patient motion. Therefore, the introduction of adaptive treatment techniques where the dose can be monitored as it is being delivered is highly desirable. We present a GPU-based dose calculation engine relying on the widely used pencil beam algorithm, developed for on-line dose calculation. The calculation engine was implemented from scratch, with each step of the algorithm parallelized and adapted to run efficiently on the GPU architecture. To ensure fast calculation, it employs several application-specific modifications and simplifications, and a fast scatter-based implementation of the computationally expensive kernel superposition step. The calculation time for a skull base treatment plan using two beam directions was 0.22 s on an Nvidia Tesla K40 GPU, whereas a test case of a cubic target in water from the literature took 0.14 s to calculate. The accuracy of the patient dose distributions was assessed by calculating the γ-index with respect to a gold standard Monte Carlo simulation. The passing rates were 99.2% and 96.7%, respectively, for the 3%/3 mm and 2%/2 mm criteria, matching those produced by a clinical treatment planning system.