A qualitative comparison of human population dynamics with some other biological populations growth in free regime is given in this paper along with a quantitative description of human population growth in the last 2000 years. It is shown that human population growth law is very different from the growth laws of other populations: all biological populations grow according to exponential law, whereas the human population grows according to hyperexponential law which essentially moves ahead of the exponential one. It is found that unlike cell populations, the differential equation of rate of human population growth is of second order. This phenomenon can be described due to accelerating function which grows simultaneously with human population number. An analytical hyperexponential equation, which allows to describe dynamics of human population, was obtained.