We used computer simulations to examine evolution of resistance to the insect growth regulator (IGR) pyriproxyfen by the sweetpotato whitefly, Bemisia tabaci (Gennadius), biotype B [=Bemisia argentifolii (Bellows & Perring)]. Consistent with trends seen in cotton (Gossipyium spp.) fields in Arizona and Israel, results suggest that evolution of resistance to pyriproxyfen may occur rapidly in this haplodiploid insect. Similar to results from models of diploid insects, resistance evolved faster with increases in toxin concentration, dominance of resistance in females, the initial frequency of the resistance allele, and the proportion of the region treated with pyriproxyfen. Resistance was delayed by fitness costs associated with resistance. Movement between treated and untreated cotton fields had little effect, probably because untreated cotton leaves provided internal refuges in treated fields and whiteflies were controlled with other insecticides in external refuges. Resistance evolved faster when susceptibility to pyriproxyfen was greater in susceptible males than susceptible females. In contrast, resistance evolved slower when susceptibility to pyriproxyfen was greater in resistant males than resistant females. Results suggest that growers may be able to prolong the usefulness of pyriproxyfen by applying lower toxin concentrations and promoting susceptible populations in refuges.