Globally, 47 million children young age were wasted, 14.3 million are severely wasted and 144 million are stunted. Around 45% of deaths among children are linked to undernutrition. The impact undernutrition is more severe among children age 6–23 months as this period is critical for child development, and irreversible damages can occur due to nutritional deficiencies. Hence aimed to assess magnitude of under nutrition and associated factors among infants and young children age 6–23 months attending Minilik II hospital, Addis Ababa, Ethiopia. Hospital based cross-sectional study was conducted among 377 Infant and young children age 6–23 months were selected using simple random sampling method. Data was collected using face-to-face interview with family and anthropometric measurement was taken. The anthropometric measurements of children were evaluated using WHO standard Antro software. Descriptive statistics was used to describe the characteristics of study population. Logistic regression was fitted to identify factors associated with under nutrition. The study revealed about 34.1% of young age children were under nutrition while 28.8% of them stunted, underweight 10.2% and 4.7% of them were wasted. Working condition of mother (AOR = 6.142, 95% CI: 2.90-13.01), education status of the mother (AOR = 5.75, 95% CI : 2.621–12.624), household live in rent house (AOR = 3.03, 95% CI: 1.30–7.04), illness/disease (AOR = 5.69, 95% CI: 2.360-13.623), inappropriate complementary feeding (AOR = 3.10, 95% CI: 1.37–7.04), breast feeding, receiving vitamin A (AOR = 0.17, 95% CI: 0.08–0.34) and growth monitoring (AOR = 0.288 at 95% CI (0.14–0.58) were found to have statistically significant association with children under nutrition.