Purpose: Difficulty in understanding spoken speech is a common complaint among aging adults, even when hearing impairment is absent. Correlational studies point to a relationship between age, auditory temporal processing (ATP), and speech perception but cannot demonstrate causality unlike training studies. In the current study, we test (a) the causal relationship between a spatial–temporal ATP task (temporal order judgment [TOJ]) and speech perception among aging adults using a training design and (b) whether improvement in aging adult speech perception is accompanied by improved self-efficacy. Method: Eighty-two participants aged 60–83 years were randomly assigned to a group receiving (a) ATP training (TOJ) over 14 days, (b) non-ATP training (intensity discrimination) over 14 days, or (c) no training. Results: The data showed that TOJ training elicited improvement in all speech perception tests, which was accompanied by increased self-efficacy. Neither improvement in speech perception nor self-efficacy was evident following non-ATP training or no training. Conclusions: There was no generalization of the improvement resulting from TOJ training to intensity discrimination or generalization of improvement resulting from intensity discrimination training to speech perception. These findings imply that the effect of TOJ training on speech perception is specific and such improvement is not simply the product of generally improved auditory perception. It provides support for the idea that temporal properties of speech are indeed crucial for speech perception. Clinically, the findings suggest that aging adults can be trained to improve their speech perception, specifically through computer-based auditory training, and this may improve perceived self-efficacy.