Provided is a molten metal discharge nozzle capable of suppressing turbulence in a molten metal stream passing through an inner bore thereof, with a simple structure. A cross-sectional shape of a wall surface of the inner bore, taken along an axis of the inner bore, comprises a part or an entirety of a curved line expressed by the following formula: log(r(z))=(1/n)×log((Hc+L)/(Hc+z))+log(r(L)) (1), where: 6≧n≧1.5; L is a length of the nozzle; Hc is a calculative hydrostatic head; and r(z) is a radius of the inner bore at a position located a distance z downward from an upper end of the nozzle, wherein, in a graph where the distance z is plotted with respect to a horizontal axis (X-axis) thereof, and a pressure of molten metal at a center of the inner bore in horizontal cross-section at a position located the distance z is plotted with respect to a vertical axis (Y-axis) thereof, an approximation formula of a line on the graph is established without simultaneously including two or more coefficients having opposite signs, and wherein, on an assumption that the line is derived from an approximation formula based on a linear regression, an absolute value of a correlation coefficient of the line is 0.95 or more.