This study examined the socio-demographic factors associated with normal linear growth among pre-school children living in better-off households, using survey data from Ghana, Kenya, Nigeria, Mozambique and Democratic Republic of Congo (DRC). The primary outcome variable was child height-for-age z-scores (HAZ), categorised into HAZ≥-2SD (normal growth/not stunted) and HAZ<-2 (stunted). Using logistic regression, we estimated adjusted odds ratios (aORs) of the factors associated with normal growth. Higher maternal weight (measured by body mass index) was associated with increased odds of normal growth in Mozambique, DRC, Kenya and Nigeria. A unit increase in maternal years of education was associated with increased odds in normal growth in DRC (aOR = 1.06, 95% CI = 1.03, 1.09), Ghana (aOR = 1.08, 95% CI = 1.04, 1.12), Mozambique (aOR = 1.08, 95% CI = 1.05, 1.11) and Nigeria (aOR = 1.07, 95% CI = 1.06, 1.08). A year increase in maternal age was positively associated with normal growth in all the five countries. Breastfeeding was associated with increased odds of normal growth in Nigeria (aOR = 1.30, 95% CI = 1.16, 1.46) and Kenya (aOR = 1.37, 95% CI = 1.05, 1.79). Children of working mothers had 25% (aOR = 0.75, 95% CI = 0.60, 0.93) reduced odds of normal growth in DRC. A unit change in maternal parity was associated with 10% (aOR = 0.90, 95% CI = 0.84, 0.97), 23% (aOR = 0.77, 95% CI = 0.63, 0.93), 25% (aOR = 0.75, 95% CI = 0.69, 0.82), 6% (aOR = 0.94, 95% CI = 0.89, 0.99) and 5% (aOR = 0.95, 95% CI = 0.92, 0.99) reduced odds of normal growth in DRC, Ghana, Kenya, Mozambique and Nigeria, respectively. A child being a male was associated with 18% (aOR = 0.82, 95% CI = 0.68, 0.98), 40% (aOR = 0.60, 95% CI = 0.40, 0.89), 37% (aOR = 0.63, 95% CI = 0.51, 0.77) and 21% (aOR = 0.79, 95% CI = 0.71, 0.87) reduced odds of normal child growth in DRC, Ghana, Kenya and Nigeria, respectively. In conclusion, maternal education, weight, age, breastfeeding and antenatal care are positively associated with normal child growth. In contrast, maternal parity, employment, and child sex and age are associated negatively with normal growth. Interventions to improve child growth should take into account these differential effects.