Population of Bangladesh has been predicted with the help of an ordinary differential equation model known as logistic population model which is parameterized by growth rate along with capacity human population of Bangladesh. We use fourth order Runge-Kutta scheme for the numerical solution of the nonautonomous and non-linear model where we incorporate the growth rate as a function of time. First we test the numerical method for Bangladesh population data (1991-2006) and we find our population projection which is very good fit with the actual data. Then we implement the logistic model that gives future population projection for Bangladesh during 1996 to 2035.