This paper describes a novel alignment-free distance-based procedure for inferring phylogenetic trees from genome contig sequences using publicly available bioinformatics tools. For each pair of genomes, a dissimilarity measure is first computed and next transformed to obtain an estimation of the number of substitution events that have occurred during their evolution. These pairwise evolutionary distances are then used to infer a phylogenetic tree and assess a confidence support for each internal branch. Analyses of both simulated and real genome datasets show that this bioinformatics procedure allows accurate phylogenetic trees to be reconstructed with fast running times, especially when launched on multiple threads. Implemented in a publicly available script, named JolyTree, this procedure is a useful approach for quickly inferring species trees without the burden and potential biases of multiple sequence alignments.