This paper suggests a new randomized forecasting method based on entropy-robust estimation for the probability density functions (PDFs) of random parameters in dynamic models described by the systems of linear ordinary differential equations. The structure of the PDFs of the parameters and measurement noises with the maximal entropy is studied. We generate the sequence of random vectors with the entropy-optimal PDFs using a modification of the Ulam–von Neumann method. The developed method of randomized forecasting is applied to the world population forecasting problem.