Supercritical fluid extraction of ${eta}$-carotene from carrot was optimized to maximize ${eta}$-carotene (Y) extraction yield. A central composite design involving extraction pressure ($X_1$ 200-,100 bar), temperature ($X_2,;35-51^{circ}C$) and time ($X_1$$ 60-200min) was used. Three independent factors ($X_1,;X_2,;X_3$) were chosen to determine their effects on the various responses and the function was expressed in terms of a quadratic polynomial equation,$Y={eta}_0+{eta}_1X_1+{eta}_2X_2+{eta}_3X_3+{eta}_11X_12+{eta}_22X_3^2+{eta}_-12X_1X_2+{eta}_12X_1X_2+{eta}_13X_1X_3+{eta}_23X_2X_3,$ which measures the linear, quadratic and interaction effects. Extraction yields of ${eta}$-carotene were affected by pressure, time and temperature in the decreasing order, and linear effect of tenter point (${eta}_11$) and pressure (${eta}_1$) were significant at a level of 0.001(${alpha}$). Based on the analysis of variance, the model fitted for ${eta}_11$-carotene (Y) was significant at 5% confidence level and the coefficient of determination was 0.938. According to the response surface of ${eta}$-carotene by cannoical analysis, the stationary point for quantitatively dependent variable (Y) was found to be the maximum point for extraction yield. Response area for ${eta}$-carotene (Y) in terms of interesting region was estimated over $10,611{mu}g$ Per 100 g raw carrot under extraction.