Borehole heat exchangers (BHEs) are often used to harvest geothermal energy at shallower depths. The standard increase in temperature with depth is generally ignored. Without high quality electricity generation as with enhanced geothermal systems (EGS) there is a lack of financial incentive for drilling deeper for higher temperatures. This temperature increase, or geothermal gradient, is rarely captured by analytical BHE models for building heating and cooling. In this paper we present a new analytical model for a coaxial borehole heat exchanger (CBHE) that specifically considers geothermal gradient. We first verify our model output by comparing results with existing numerical and experimental results under the same configuration of CBHE. To further investigate our model's sensitivity towards fluid flow direction, geothermal gradient, and borehole thermal resistance, we also compare the temperature distributions and rate of heat gain/loss along the flow direction within the entire proposed CBHE. We identify the best flow direction with annulus as inlet in heat extraction mode, confirm positive influence of increasing geothermal gradients towards the heat extraction, and confirm a nonlinear correlation between the borehole thermal resistance with the output fluid temperature and amount of heat extracted. This study can provide a useful analytical simulation tool and important guide to design of CBHE. (C) 2019 Published by Elsevier Ltd.