A number of studies have concluded that dreaming is mostly caused by randomly arriving internal signals because "dream contents are random impulses", and argued that dream sleep is unlikely to play an important part in our intellectual capacity. On the contrary, numerous functional studies have revealed that dream sleep does play an important role in our learning and other intellectual functions. Specifically, recent studies have suggested the importance of dream sleep in memory consolidation, following the findings of neural replaying of recent waking patterns in the hippocampus. The randomness has been the hurdle that divides dream theories into either functional or functionless. This study presents a cognitive and computational model of dream process. This model is simulated to perform the functions of learning and memory consolidation, which are two most popular dream functions that have been proposed. The simulations demonstrate that random signals may result in learning and memory consolidation. Thus, dreaming is proposed as a continuation of brain's waking activities that processes signals activated spontaneously and randomly from the hippocampus. The characteristics of the model are discussed and found in agreement with many characteristics concluded from various empirical studies.