This paper proposes a method of estimating and simulating a maximum entropy distribution given moment conditions based on MonteCarlo approach. The method provides an simple alternative to conventional calculation methods of maximum entropy densities which involve complex numerical integration and are subject to occasional failure. We first show that maximum entropy density on a random sample converges to minimum cross entropy solution to the sample density. Using this result, we show that the empirical maximum entropy density on a uniform sample supported within sufficiently large boundary converges to the true maximum entropy density. The performance of the proposed method is checked by several examples.