Whereas many studies of implicit memory concentrated on whether conscious/intention to be remembering of retrieve or not, they seldom referred on the intention of encoding. In this study, we focus on the effect of intentional and incidental encoding on implicit and explicit memory. In experiment 1, a forced-forgetting task was set as incidental learning situation. 40 participants were divided into three groups and were tested for word fragment, cued recall and recognition task. In the word fragment task, the forgetting curve indicated that incidental implicit memory was retained longitudinally, but showed partial inhibit effect that first took a down trend and went up again. Also, cued recall task and recognition task showed long-term retention of memory by forced-forgetting. In experiment 2, 31 participants were divided into three group tested for word fragment task, cued recall task and recognition task where foveal vision was set as intentional learning and peripheral vision as incidental learning. As a result of word fragment task, it was suggested that the forgetting curve of implicit memory by incidental learning drew an U-shape curve. Also, the record of cued recall task and recognition task, as well as experiment 1, showed long-range retain of memory by incidental learning. In experiment 3, 41 participants were tested for word fragment task in which figure-treat task was set as incidental-learning situation. The result showed, like experiment 1, 2, an U-shape forgetting curve in incidental learning condition. The findings suggest that the U-shaped forgetting curve are robust in various incidental-learning situations.