Previous studies have shown that the HIV-1 epidemic in Cuba displayed a complex molecular epidemiologic profile with circulation of several subtypes and circulating recombinant forms (CRF); but the evolutionary and population history of those viral variants remains unknown. HIV-1 pol sequences of the most prevalent Cuban lineages (subtypes B, C and G, CRF18_cpx, CRF19_cpx, and CRFs20/23/24_BG) isolated between 1999 and 2011 were analyzed. Maximum-likelihood analyses revealed multiple introductions of subtype B (n≥66), subtype C (n≥10), subtype G (n≥8) and CRF18_cpx (n≥2) viruses in Cuba. The bulk of HIV-1 infections in this country, however, was caused by dissemination of a few founder strains probably introduced from North America/Europe (clades B(CU-I) and B(CU-II)), east Africa (clade C(CU-I)) and central Africa (clades G(CU), CRF18(CU) and CRF19(CU)), or locally generated (clades CRFs20/23/24_BG). Bayesian-coalescent analyses show that the major HIV-1 founder strains were introduced into Cuba during 1985-1995; whereas the CRFs_BG strains emerged in the second half of the 1990s. Most HIV-1 Cuban clades appear to have experienced an initial period of fast exponential spread during the 1990s and early 2000s, followed by a more recent decline in growth rate. The median initial growth rate of HIV-1 Cuban clades ranged from 0.4 year⁻¹ to 1.6 year⁻¹. Thus, the HIV-1 epidemic in Cuba has been a result of the successful introduction of a few viral strains that began to circulate at a rather late time of the AIDS pandemic, but then were rapidly disseminated through local transmission networks.