To evaluate the potential role of Aedes albopictus (Skuse) as a vector of Zika virus (ZIKV), colonized mosquitoes of low generation number (≤ F5) from Brazil, Houston, and the Rio Grande Valley of Texas engorged on viremic mice infected with ZIKV strains originating from Senegal, Cambodia, Mexico, Brazil, or Puerto Rico. Vector competence was established by monitoring infection, dissemination, and transmission potential after 3, 7, and 14 days of extrinsic incubation. Positive saliva samples were assayed for infectious titer. Although all three mosquito populations were susceptible to all ZIKV strains, rates of infection, dissemination, and transmission differed among mosquito and virus strains. Aedes albopictus from Salvador, Brazil, were the least efficient vectors, demonstrating susceptibility to infection to two American strains of ZIKV but failing to shed virus in saliva. Mosquitoes from the Rio Grande Valley were the most efficient vectors and were capable of shedding all three tested ZIKV strains into saliva after 14 days of extrinsic incubation. In particular, ZIKV strain DakAR 41525 (Senegal 1954) was significantly more efficient at dissemination and saliva deposition than the others tested in Rio Grande mosquitoes. Overall, our data indicate that, while Ae. albopictus is capable of transmitting ZIKV, its competence is potentially dependent on geographic origin of both the mosquito population and the viral strain.