Cocaine addiction is a chronic disorder in which the person loses control over drug use. The past memories of the stimuli associated with the drug are a relevant clinical problem, since they trigger compulsive drug seeking and taking habits. Furthermore, these persistent drug-related memories seemingly coexist with cognitive decline that predicts worse therapeutic output. Here we use a new animal model of cocaine-altered cognition that allowed to observe these events in the same individual and study their relationship. Mice were chronically administered cocaine in a conditioned place preference (CPP) apparatus for 14 days, and control mice received saline. After 28 days of cocaine withdrawal, animals were tested for retrieval of remote drug-associated memory as well as for cognitive performance in a battery of tests, including novel object and place recognition and spatial memory. The cocaine-withdrawn mice showed persistent CPP memory while impaired in the cognitive tasks, displaying deficits in reference memory acquisition and working memory. However, the CPP expression was not associated to the defective cognitive performance, indicating that they were concomitant but independent occurrences. After completion of the experiment, adult hippocampal neurogenesis (AHN) was studied as a relevant neurobiological correlate due to its potential role in both learning and drug addiction. Results suggested a preserved basal AHN in the cocaine-withdrawn mice, but an aberrant learning-induced regulation of these neurons. This paradigm may be useful to investigate maladaptive cognition in drug addiction as well as related therapies.