A Monte Carlo convolution method for simulating time-correlated single photon counting data is presented. The random convolution automatically produces the Poisson statistics of the real experiment. The new simulation technique offers realistic treatment of various aspects of the single photon counting experiment, including pulse pileup. The random convolution is also incorporated in a data analysis technique using a reference fluorophore. Illustrative examples comparing the Monte Carlo and conventional simulation methods are given and the conceptual differences are discussed.