In this work, a simple and efficient numerical approach to determine the shape of the minimum-drag axisymmetric forebody in inviscid supersonic flow with an attached shock constraint has been described. Taylor–Maccoll equation in conjunction with the tangent cone method is employed to estimate the pressure drag coefficient which is also chosen as the cost function. The forebody geometry is parameterized using a Non-Uniform Rational B-Splines (NURBS) curve whose control points are the design variables for optimisation using the steepest descent algorithm. Numerical studies demonstrate that the optimal forebody geometry for a given length and base radius has as much as 15 % lesser drag, depending on the Mach number than a cone of the same fineness ratio and that the convergence to the optimal solution exhibits a relatively weak Mach-number dependence. © 2014, The Institution of Engineers (India).