The effect of overconfidence and demand uncertainty in inventory system is studied. In order to depict the decision-maker’s overconfidence, a mean-increasing and variance-decreasing transformation is introduced. The monotonicities of the optimal order quantity and optimal profit on penalty cost and the overconfident level are obtained. It is proved that the larger demand leads to the high optimal order quantity, and the optimal order quantity has stochastic monotonicity under the cut criterion order. The corresponding sufficient conditions and/or necessary and sufficient conditions are given. Furthermore, by using standardized random variable transformation, it is proved that profit will decrease when the demand variability increases in the high profit condition.