Segmental duplications are enriched within many eukaryote genomes, and their potential consequence is gene duplication. While previous theoretical studies of gene duplication have mainly focused on the gene silencing process after fixation, the process leading to fixation is even more important for segmental duplications, because the majority of duplications would be lost before reaching a significant frequency in a population. Here, by a series of computer simulations, we show that purifying selection against loss-of-function mutations increases the fixation probability of a new duplicate gene, especially when the gene is haplo-insufficient. Theoretically, the probability of simultaneous preservation of both duplicate genes becomes twice the loss-of-function mutation rate (u(c)) when the population size (N), the degree of dominance of mutations (h) and the recombination rate between the duplicate genes (c) are all sufficiently large (Nu(c)>1, h>0.1 and c>u(c)). The preservation probability declines rapidly with h and becomes 0 when h=0 (haplo-sufficiency). We infer that masking deleterious loss-of-function mutations give duplicate genes an immediate selective advantage and, together with effects of increased gene dosage, would predominantly determine the fates of the duplicate genes in the early phase of their evolution.