Consider a continuous-time stochastic model in which species arrive in the sample according to independent Poisson processes and where the species discovery rates are heterogeneous. Based on an initial survey, we are concerned with the problem of predicting the number of new species that would be discovered by additional sampling. When the sampling time or sample size of the additional sample tends to infinity, this problem reduces to the prediction of the number of undetected species in the original sample, or equivalently, the estimation of species richness. The topic has a wide range of applications in various disciplines. We propose a simple prediction method and apply it to two datasets. One set of data deals with the capture counts of the Malayan butterfly and the other set deals with identification records of organic pollutants in a water environment. Simulation results are shown to investigate the performance of the proposed method and to compare it with the existing estimators.