A population consisting of women who have conceived before a time t ignores all women whose conception time exceeds t. Such a population is considered as a truncated population, and the samples are called truncated samples. Under the assumption that fecundability among women varies according to a Beta distribution (with parameters a and b), the distribution of conception times in a truncated population can be considered as truncated Type I geometric. This paper presents an algorithm to obtain the moment and maximum likelihood estimates of a and b from the truncated samples. Large sample properties of the estimators are also studied. Examples using the Hutterite and the Princeton Fertility Survey data are given.