The coefficient of performance and specific heating load of an irreversible three-heat-source heat pump are given by using a general cycle model affected by the finite-rate heat transfer, heat leak and internal irreversibility of the cyclic working fluid. The heat pumping load divided by the total cost per unit time is taken as a new objective function and used to investigate the performance of the heat pump. The thermoeconomic and thermodynamic performance characteristics of the heat pump are discussed in detail. Some important performance parameters such as the thermoeconomic objective function and coefficient of performance are optimized. The optimally operating regions of the heat pump and the bounds of several performance parameters are determined. Finally, it is pointed out that the Carnot heat pump may be taken as a special case of a three-heat-source heat pump and consequently its optimal performance can be directly derived from the results obtained here. (c) 2005 Elsevier Ltd. All rights reserved.