Evolutionary transitions among maternal, paternal, and bi-parental care have been common in many animal groups. We use a mathematical model to examine the effect of male and female life-history characteristics (stage-specific maturation and mortality) on evolutionary transitions among maternal, paternal, and bi-parental care. When males and females are relatively similar – that is, when females initially invest relatively little into eggs and both sexes have similar mortality and maturation – transitions among different patterns of care are unlikely to be strongly favored. As males and females become more different, transitions are more likely. If females initially invest heavily into eggs and this reduces their expected future reproductive success, transitions to increased maternal care (paternal → maternal, paternal → bi-parental, bi-parental → maternal) are favored. This effect of anisogamy (i.e., the fact that females initially invest more into each individual zygote than males) might help explain the predominance of maternal care in nature and differs from previous work that found no effect of anisogamy on the origin of different sex-specific patterns of care from an ancestral state of no care. When male mortality is high or male egg maturation rate is low, males have reduced future reproductive potential and transitions to increased paternal care (maternal → paternal, bi-parental → paternal, maternal → bi-parental) are favored. Offspring need (i.e., low offspring survival in the absence of care) also plays a role in transitions to paternal care. In general, basic life-history differences between the sexes can drive evolutionary transitions among different sex-specific patterns of care. The finding that simple life-history differences can alone lead to transitions among maternal and paternal care suggests that the effect of inter-sexual life-history differences should be considered as a baseline scenario when attempting to understand how other factors (mate availability, sex differences in the costs of competing for mates) influence the evolution of parental care.