With the rapid growth of entire genome data, phylogenomics focuses on analyzing evolutionary histories and relationships of species, i.e., the tree of life. For decades it has been realized that the genome-wide phylogenetic inference can be approached based upon the dynamic pattern of gene content (the presence/absence of gene families), or extended gene content (absence, presence as a single-copy, or duplicates). Those methods, conceptually or technically, invoked the birth-and-death process to model the evolutionary process (gene duplication or gene loss. One common drawback is that the mechanism of new gene input, including de novo origin of new genes and the lateral gene transfer, has not been explicitly considered. In this paper, the author developed a new genome distance approach for genome phylogeny inference under the origin-birth-death stochastic process. The model takes gene duplication, gene loss and new gene input into account simultaneously. Computer simulations found that the two-genome approach is statistically difficult to distinguish between two proliferation parameters, i.e., the rate of gene duplication and the rate of new gene input. Nevertheless, it has also demonstrated the statistical feasibility for using the loss-genome distance to infer the genome phylogeny, which can avoid the large sampling problem. The strategy to study the universal tree of life was discussed and exemplified by an example.