We consider an in nite-allele Markov branching process (IAMBP). Our main focus is the frequency spectrum of this process, i.e., the proportion of alleles having a given number of copies at a speci ed time point. We derive the variance of the frequency spectrum, which is useful for interval estimation and hypothesis testing for process parameters. In addition, for a class of special IAMBP with birth and death o spring distribution, we show that the mean of its limiting frequency spectrum has an explicit form in terms of the hypergeometric function. We also derive an asymptotic expression for convergence rate to the limit. Simulations are used to illustrate the results for the birth and death process.