In the solar absorption cooling systems, concentrating collector can be adopted to achieve higher driven temperature and improve the system performance. The Compound Parabolic Concentrator (CPC) is a good option with both concentrating and stationary features. With higher working temperature, solar absorption cooling system with concentrating collector has more choices of absorption chillers than the system with non-concentrating collector. The aim of this paper is to find the better chiller choice for solar absorption cooling systems with CPC. The analyzed LiBr-water absorption chillers include the single effect chiller, the double effect absorption chiller and a novel variable effect chiller built by the author. Simulation is carried out in TRNSYS. Model of the variable effect absorption chiller is first derived from MATLAB artificial neural network (ANN) toolbox based on experimental data, and then built in TRNSYS. Performance of the three systems is calculated under the same condition. Performance of the three systems is compared to get the better choices. The impacts of the solar collector area, cutoff driven temperature and storage tank volume on the solar cooling fraction, auxiliary heat input, average chiller COP and average solar efficiency are analyzed. The variable effect system has high solar cooling fraction, low auxiliary heat input and high solar efficiency. The single effect system has medium solar fraction, high auxiliary heat input and medium solar efficiency. The double effect system has low solar cooling fraction, low auxiliary heat input and low solar efficiency.