The second-fastest-growing category is expected to be solo fathers, at 1.5 per cent a year, but this is also the smallest category, with a projection that there will be 57,000 of these families in 2038.
Two-parent families are expected to remain the second-largest type by 2018 - at 613,000.
This set of projections assumes medium fertility, mortality and migration.
Statistics NZ said: "There are more couple-without-children families than other family types. Couple-without-children families include couples with no children and couples who have children living elsewhere."
"Couples whose children have left the parental home - the empty-nesters - are expected to be the most significant factor in the growth of couple-without-children families," said Peter Dolan, the senior manager for population statistics.
"An increasing proportion of couples who will never have children is also likely to
contribute to the growing number of this group of families, but to a much lesser extent."
"Medium" projections for the numbers of families, broken down by type of family, 2013-2038. Source: Statistics NZ
The agency said childless couples account for more than half the projected growth in the number of families; and two-parent families account for one-third.
In 2013, 41 per cent of families were couples without children. This is projected to increase to 45 per cent of families by 2038.
Two-parent families are expected to shrink, from 40 per cent of families, to 38 per cent.
One-parent families account for the smallest portion of growth of all families. Eighteen per cent of families in 2013 were one-parent families and this is expected to decrease to 17 per cent in 2038.
One-parent families with a male parent are projected to increase from 18 per cent of one-parent families in 2013 to 22 per cent of one-parent families in 2038.
One-parent families can include elderly parents who are dependent on their child as well as younger parents with dependent children.
The projections indicate that between 2013 and 2038:
• The number of families and households will grow faster than the population, which is projected to increase by an average of 1.1 per cent a year between 2013 and 2038.
• The number of households is projected to increase by an average of 1.2 per cent a year, from an estimated 1.65 million households in 2013 to 2.2 million by 2038 (an increase of 596,000).
• One-person households are projected to increase by an average of 1.7 per cent a year, from 393,000 in 2013 to 599,000 in 2038.
• The average size of households will decrease to 2.51 people by 2038, from 2.64 people in 2013.
• The number of families is projected to increase by an average of 1.2 per cent a year, from an estimated 1.25 million families at 30 June 2013 to 1.68 million by 2038 (an increase of 433,000).
• Couples-without-children families will increase by an average of 1.6 per cent a year. They will remain the most common family type.