Measurement uncertainty reports are widely used in metrology. It is very important to utilize uncertainty information effectively which is within the term of validity to the future uncertainty measurement. It proposes a methodology which combining the principle of maximum entropy and the Heaviside step function to determine the distribution of measurand with the constraints of prior uncertainty information. The genetic algorithm is given to optimize the computation of Lagrange multiplier at the same time. It has been proven that the maximum entropy distribution based on the uncertainty information and the theoretical distribution are almost overlapped in the case of symmetric distribution, but there is a certain deviation between the two distributions for the situation of asymmetric distribution. However, the maximum entropy distribution is an appropriate approximation to the measurand true distribution if only the prior measurement uncertainty information is known, and it can be useful when the measurand is participated in the further measurement uncertainty evaluation.