The maximum entropy (maxent) approach provides an attractive and appealing method for obtaining a probability distribution in some limited information environments. The maxent approach, however, is not easy to use for practical application since analytic derivation of a maxent density is usually not feasible. This paper proposes a method of estimating and simulating an maxent density. It is a numerically tractable and stable method that is relatively simple in real computation. The proposed method is capable of handling problems for which existing methods are difficult to apply or are subject to occasional failure. Monte Carlo results confirm that the proposed method can be well applied for cases when existing methods are subject to occasional failure.