CdTe is one of the most promising materials for thin-film solar cells. However, further improvement of its performance is hindered by its relatively short minority-carrier lifetime. Combining theoretical calculations and experimental measurements, we find that for both intrinsic CdTe and CdTe solar cell devices, longer minority-carrier lifetimes can be achieved under Cd-rich conditions, in contrast to the previous belief that Te-rich conditions are more beneficial. First-principles calculations suggest that the dominant recombination centers limiting the minority-carrier lifetime are the Te antisite and Te interstitial. Therefore, we propose that to optimize the solar cell performance, extrinsic p-type doping (e.g., N, P, or As substitution on Te sites) in CdTe under Cd-rich conditions should be a good approach to simultaneously increase both the minority-carrier lifetime and hole concentration.