A fast computation of PSDs in fluidized beds is a basic requirement for the mathematical modelling of the behaviour of fluidized beds as it is the most time consuming step in the complete prediction procedures. In an attempt to remove this bottleneck, a computationally efficient approach for the solution of population balance of Kunii and Levenspiel is developed. This new approach replaces the conventional numerical integration of the analytical solution of the population balance with direct integration in ordinary differential equation (ODE) form by using a powerful integrator, LSODE (Livermore Solver for Ordinary Differential Equations). The input data required for the prediction of PSDs were taken from a pilot size fluidized bed combustor burning low calorific value lignite with wide size distribution. The results obtained by direct solution of the ODE were found to be as accurate as the analytical solution. Comparison of the CPU times shows that the time required for the new solution is at least two orders of magnitude smaller than that required by the analytical solution for the same number of intervals in particle size and that the CPU time increases from 280 to 17 112 s when the number of intervals in particle size changes from 100 to 400 for the analytical solution while it remains almost constant at 4 s for the direct integration on an IBM RISC/6000 computer.