Vertically aligned carbon nanotube field-effect transistors (CNTFETs) have been experimentally demonstrated (J. Li et al., Carbon, 2012, 50, 4628-4632). The source and drain contact heights in vertical CNTFETs could be much higher than in flat CNTFETs if the fabrication process is not optimized. To understand the impact of contact height on transistor performance, we use a semi-classical method to calculate the characteristics of CNTFETs with different contact heights. The results show that the drain current decreases with increasing contact height and saturates at a value governed by the thickness of the oxide. The current reduction caused by the increased contact height becomes more significant when the gate oxide is thicker. The higher the drain voltage, the larger the current reduction. It becomes even worse when the band gap of the carbon nanotube is larger. The current can differ by a factor of more than five between the CNTEFTs with low and high contact heights when the oxide thickness is 50 nm. In addition, the influence of the contact height is limited by the channel length. The contact height plays a minor role when the channel length is less than 100 nm.