Various reliability methods have been suggested in the literature, but the bound of an estimated reliability has received less attention. The maximum entropy principle is used to obtain the reliability bound with respect to the first moment truncated for the first time. Compared to the previous methods of probability bounding based on given moments, our method is demonstrated to generate a tight upper bound that is practically useful for engineering applications. Numerical examples have shown that a good upper bound of probability of failure is well obtained up to four given moments, but with more moments a divergence problem can occur.