This pilot study was conducted to test whether conceptual learning for young children could be accelerated or not. The subjects were 153 kindergarten children. They were taught to learn some new concepts which they did not have at first. Then, they were given opportunities to transfer the new learned concepts to some similar situations, till they "understood" these concepts. At last, these accelerated children were confronted by a situation which was designed to "torpedo" or "destroy" the new learned concepts. It was hypothesized that the acceleration is not successful if, when torpedoed, the children returned to think in old ways and failed to maintain new ways of thinking. Results of four kinds of experiments (Number Conservation, Volumn Conservation, Quantity Conservation, and Magnetic Conceptual Learning) seemed to support Piaget's notion that the cognitive development of the young children are more or less age-related and therefore is not easily accelerated. Since this was a report of pilot study, some ways to attach this problem were suggested and no conclusion was drawn.